Counting problem Definition and 57 Threads

Suppose you pick a k-element subset of {1, 2, ..., n}, call it A. How many of the other k-element subsets have k-1 elements in common with A? I've been at this for quite some time, but I always overcount. Can anyone help me out? My last attempt gave me (n-k+1)k - \frac{k(k-1)}{2}, which isn't...

Hello everyone, I'm having some issues on this problem: A coin is tossed ten times. In each case the outcome H (for heads) or T (for tails) is recorded. (One possible outcome of the ten tossings is denoted THHTTTHTTH.) I got a, d right i believe. but I need someone to check if i did the...

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...

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

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...

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?