Tricky inclusive numbersHomework

[tae3001]

A 5 digit number is one between 10,000 and 99,999 inclusive
1. How many 5 digits numbers are therE?
2. HOW MANY CONSISTOF 5 DISTINCT DIGITS?
3. hOW MANY 5 DIGIT NUMBERS CONTAIN AT LEAST ONE ODD DIGIT?

 

[Hurkyl]

You don't need to shout.

So, what have you tried?

 

[tae3001]

oops sorry..(LOL)
well first i did..
10,000-99,999 +1 =90000 thast question 1

I am stuck with question 2 and 3.. I want to divide by 5 or subtract.. but Iam warped//..

 

[xanthym]

A 5 digit number is one between 10,000 and 99,999 inclusive
1. How many 5 digits numbers are therE?
2. HOW MANY CONSISTOF 5 DISTINCT DIGITS?
3. hOW MANY 5 DIGIT NUMBERS CONTAIN AT LEAST ONE ODD DIGIT?

(Note: In the following discussion, "Digit #1" is the LEFTMOST digit.)
SOLUTION HINTS:
2) → For 5 distinct digits, you have 9 choices for the 1st digit, 9 for the 2nd, 8 for the 3rd, 7 for the 4th, and 6 for the 5th. ⇒ ⇒ {Total Number}={? x ? x ? x ? x ?}.
3) → The numbers having at least 1 odd digit would be those left over after removing numbers having all even digits. In other words, {90,000 - (?)}. For the number having all 5 even digits, remember that digit #1 can be any of {2, 4, 6, or 8 ⇒ 4 choices}, and digits #2 thru #5 can be any of {0, 2, 4, 6, or 8 ⇒ 5 choices}.


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[tae3001]

i am starting to see it.. but where would I select the distinct digits?? from 90,000 or would i choose
89999,89998,89997 and so on?
or would I take them from 10,000 and 99,999?

 

[xanthym]

i am starting to see it.. but where would I select the distinct digits?? from 90,000 or would i choose
89999,89998,89997 and so on?
or would I take them from 10,000 and 99,999?

(In the following discussion, "Digit #1" is the Leftmost digit.)

Problem #2:
Digit #1 (Leftmost) is chosen from the set {1, 2, 3, 4, 5, 6, 7, 8, 9 ⇒ 9 choices}, and Digits #2 thru #5 are chosen from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ⇒ 10 choices}, with the provision that each digit is distinct (different).
Thus, Digit #1 has 9 choices, Digit #2 has 9 choices {=(10 - 1) after eliminating #1's choice}, Digit #3 has 8 choices {=(10 - 2) after eliminating #1's & #2's choices}, Digit #4 has 7 choices {=(10 - 3) after eliminating #1's, #2's, & #3's choices}, and Digit #5 has 6 choices {=(10 - 4) after eliminating #1's, #2's, #3's, & #4's choices}.
{Total # of Numbers from 10000 to 99999 with All Distinct Digits} =
= (9)x(9)x(8)x(7)x(6) = (27216)

Problem #3:
The numbers having at least 1 odd digit would be those left over after removing numbers having all even digits. In other words, {90,000 - (# with All Even Digits)}. For the number having all 5 even digits, Digit #1 can be any of {2, 4, 6, or 8 ⇒ 4 choices}, and Digits #2 thru #5 can be any of {0, 2, 4, 6, or 8 ⇒ 5 choices}.
{Total # of Numbers from 10000 to 99999, inclusive, with At Least 1 Odd Digit} =
= 90000 - {(4)x(5)x(5)x(5)x(5)} = (87500)


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