Probability problem

[skhan]

Bill has one of each of these cards (5 cards) : 1, 3, 5, 7 , 9
How many three digit numbers divisible by three can he make with his cards ?

 

[Harry_the_cat]

Hint: A three digit number is divisible by 3 if the sum of the digits is divisible by 3.

 

[pka]

Bill has one of each of these cards (5 cards) : 1, 3, 5, 7 , 9
How many three digit numbers divisible by three can he make with his cards ?

LOOK at reply #2. There are \(\displaystyle \binom{5}{3}=10\) sets of those three digits each of those sets can be arranged in six ways.
Consider the set \(\displaystyle \{1,3,5\}\) the sum of those three is nine which is dividable by three. So now we have six.
Can you finish?