Counting Definition and 392 Threads

i have discovered a formula for \pi(x^{a}) being Pi the prime number counting function in terms of a triple integral...but you wll say..this is already made what is this good for?..in fact if you knew \pi(x^{a}) with a total error O(x^d) by setting a=Ad and making A--->oo (infinite) the total...

This question seems easy, but I don't understand what it's mean with "without making change". Could someone help me? If you have 2 dollars, 2 quarter and 3 nickels: a) how many different sums can you pay without making change? b) Change the quarters into dimes and answer again...

Could someone help me with this question ? There are two locks on the door and the keys are among the six different ones you carry in your pocket. In a hurry you dropped one somewhere. a) What is the probability that you can still open the door ? b) What is the probability that the...

Could someone help me with this question ? There are two locks on the door and the keys are among the six different ones you carry in your pocket. In a hurry you dropped one somewhere. a) What is the probability that you can still open the door ? b) What is the probability that the...

I tried to write a function that would count all possible combinations that 4 couples could sit at a table assuming no man can sit next to his wife or next to another man. and 1wife and 1 husband sit at fixed positions. my problem doesn't compile and it says i either have too many or too few...

hmmmmmmmmmmm consider u r driving a train. there is 100 passengers in the train. at first station 50 more get into the train. 2nd station 27 more come in. but at the third station 45 left the train. 4th station no one leave or enter... 5th station 37 ins and 49 out. what is the name of...

I'm taking a crack at learning probability and statistics starting from the basics. Anyways here is the question. --- A fair coin is tossed 10 times and the sequence of scores recorded. How many sequences are there? How many sequences are there that contain exactly 3 heads? ---...

Hi everyone, I need to write a C code program to count the # of fuctions used in a certain file (function counter) Can you guys give me some hints/suggestions/ideas ? Thanks, Stan

I have encountered this set problem that seems simple enough at first glance, but I'm pretty ignorant about formal set theory and unsure of the rules. As I encountered it, this is how it was written: For any set S let P(S) denote all subsets of S. For example S={1,2} Then P(S)= {Ø, {1}...

I'm obviously not going to ask how many strings there are in the universe. :wink: my question. To each quark how many strings are there? Just one unique one? Billions and Billions? Also does Brian Greene's book. "The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for...

thare are 8 candidates for three student seats how many different ways can the seats be chosen? With the FCP I get 24 If it is a permutation I get 336 which is right and why? Thanks for the help

The kyoto Clock http://www.junkscience.com/

Is it fair to say combinations are just an application of the counting principle? I already understand that permutations are just an application of fundamental principle and that combinations are just an application of permutations. If it's fair to say that combinations are in fact, just an...

Is it fair to say combinations are just an application of the counting principle? I already understand that permutations are just an application of fundamental principle and that combinations are just an application of permutations. If it's fair to say that combinations are in fact, just an...

Hi, I wasn't sure how to approach this problem: You have 5 differently colored stones-red, orange, blue, green, purple. If the green stone cannot be placed at the front or the back of the sequence, how many possible arrangements can you make? I know that without the above restriction, the...

You have 10 pink balls and 15 purple balls. How many distinguishable arrangements are possible if two pink balls cannot be next to each other? I know the answer is 8008 but I have no idea how to get this

hi everyone... how many arrangements of this word "aabbcccdddd" is possible if we only use 3 of them? I know if we could use all of them it would just be 11!/(2!2!3!4!), but what if we only use 3? :confused: Thanks in advance

show that \frac{ ((n^2)!)!}{(n!)^{n+1}} is an integer. i was thinking of saying that there are so many people who can be put on a committee, etc etc which would make an integer. i don't think this is real hard but nothing is really jumping out at me

Is there a concise, easily calculable way to count the sum of all the paths from the lower left corner of a square of integer size to the upper right corner where you only move up or right in steps of 1 unit, PLUS all the partial paths? i.e. if you have a city with roads in a 10x10 grid (100...

The question is... How many subsets of a (2n+1)-element set have n elements or less? To figure this out I started by using a workable example. Obviously n must be small to keep the total number of subsets small. So I started with n=1 and so there are 8 total subsets. And of course in...

Is there a systematical way to count all the possible feynman diagram with vertices less than or equal to n...

1) If X is an n-element set and Y is an m-element set, how many functions are there from X to Y? I am not sure but I worked on this for a while and I come up with there are m^n possible functions. 2) There are five distinct computer science books, three distinct mathematics books and...

Prove: a group of even order must have an even number of elements of order 2

OK I'm unclear about how to use FCP to solve this problem: The final score in a hockey game is 5-2. How many different scores are possible at the end of the second period? :confused:

Problem details: I think if I pretend that N is also a number from 0-9, then there would be P(10, 7) numbers without repeats, but then that's too much and I'm not sure how I can subtract the number's that N is not supposed to have. The other way I was thinking is the last 6 numbers can be...

I refer you to a proposal about the finiteness of the integers: http://paulandellen.com/essays/essay089.htm How could this be? Everyone has assumed that the integers are infinite, yet a proof can be give to illustrate otherwise. Firstly we will use the characters necessary for expression of...

Here are my problems: 1) Suppose seven school children (3 girls and 4 boys) are lined up to board a school bus. Find the number of ways they could line up if no two boys are together. This arrangement would be BGBGBGB. So if I consider each BG as a unit, then there are 4! arrangements. But...

dear reader, here is a quick counting question: A counter near a long-lived radioactive source measures an average of 100 counts per minute. The probabilty that more than 110 counts will be recorded in a given one-minute interval is most nearly (A) zero (B) .001 (C) .025 (D) .15 (E) .5 I...

Dear members, here is a gre problem that I couldn't know how to tackle, any effort will be greatly appreciated. An experimenter measures 9934 counts during one hour from a radioactive sample. From this number the counting rate of the sample can be estimated with a standard deviation of most...

A set of blocks contains blocks of heights 1, 2, and 4 inches. Imagine constructing towers of piling block of different heights directly on top of one another. Let t(n) be the number of ways to construct a tower of height n inches. Find a recurrence relation for t(1), t(2), t(3)... Here's...

How many 16-bit strings contain exactly nine 1's? I said the total number is 2 to the 16th power, so to get half with 1's would be 2 to the 8th, or 256. How many 16-bit strings contain at least fourteen 1's? I have no idea. When determining a how to get 2 pair in a poker hand, why is...

Hexadecimal numbers are made using the sixteen digits 0 - 9, A-F. how many hexadecimal numbers are there between the hexadecimal numbers 30 and AF? There are 8 numbers between 3 and A, so I got 3 x 16, but I don't really know.

I can't seem to put the Fundamentals of Counting to good use... I have such a hard time answering probability questions with the rules of counting. Here's one question that blew my mind: There are 4 persons. The sample space E consists of the events E={E1, E2, E3, E4, E5 }. Let E1 be the...

Here's an old one: starting with 0 (or 1) list all the natural numbers using nothing but 4 4s. I'll go first. 0 = (4 - 4)/(4*4) 1 = (4*4)/(4*4) 2 = (4*4)/(4*sqrt(4)) ... etc

The question is how many 8-bit strings have either the second or the fourth bit 1 (or both)? I know the soulution is 3*2^6 but why?? Also this question how many 8 bit strings begin and end with 1? is it 8C2?

Having a lot of trouble with this problem as well: How many integers less than 500 are relatively prime to 500? I know that when two numbers are relatively prime, that means that the greatest common divisor of those two numbers is 1. But I can't figure out a formula that uses sets in order...

I have some questions about counting principles in mathematics: If I had standard deck of 52 playing cards, then a. How many ways can one draw a heart or a spade? b. " " an ace or a king? c. " " a card numbered 2 through 10? d. " " a card numbered 2 through 10 or a king? I got these answers...

I think i got this answer. How many ways are there to distribute five distinguishable objects into three indistinguishable boxes? Wouldn't the answer just be C(5,3) because the boxes are indistinguishable? Or do i treat this question the same as if the boxes were distinguishable?

A general two digit counting number is: d1*b + d0 = C ; where C is the count Let b = 2 as an example d 1 0 C ------ 0 0 0 0 1 1 1 0 2 1 1 3 b is the count of symbols in the digit, but it can start at 0 d1*0 + d0 = C ; works fine d0 = C ; and can be any base. d 1 0 C...

The dial on a 3 number combination lock contains markings to represent the numbers from 0 to 59. How many combinations are possible if the first and second numbers differ by 3? What I did was: 1st number: It can be any of the 60 numbers (if we take 0 also as a #) 2nd number: I think since...

is there an easier way of knowing how to count certain sequences in a problem using the same concept, i mean there are formulas but how do we tell which one we should use.

Hello all! First of all, please excuse me for barging in on you all like this. I am a nobody with little formal education in ANY field and I apologize if I seem a little mad. The bottom line is this - I just CANNOT find any satisfactory answers to my questions across the whole of the net and...