Expert: Paul Klarreich - 10/15/2010

Question
a 3 digit number is to be formed from the nmbers 3,4,5,6,7 (repetition not allowed).Find the probability thatthe number is divisible by 3.
i found this harder to do then say divisible by 5.

Answer
Questioner:   athena
Country:  Australia
Category:  Advanced Math
Private:  No
 
Subject:  probability
Question:  a 3 digit number is to be formed from the nmbers 3,4,5,6,7 (repetition not allowed).Find the probability thatthe number is divisible by 3.
i found this harder to do then say divisible by 5.
....................................................
Here is the clue, mate:

An integer is divisible by 3 if the sum of its digits is divisible by 3.  So:

357 (sum of digits is 15) and all permutations thereof is divisible by 3.
457 (sum of digits is 16) and all permutations thereof is not divisible by 3.

There are C(5,3) combinations to consider.  (Yes, I said combinations.)
That is only 20, so you can simply list them and check each.