Probability

Question

A die is thrown 3 times and sum of 3 number thrown is 15 . find the chance that first throw was a 4 ?

Comments

i am getting 1/5 as answer is it correct ?

Answer 1

Possible combination for sum (15) = Permutations of  {(6,6,3) (6,5,4) (5,5,5)}
Number of Combinations in which Sum is 15 = 3!/2! + 3! + 3!/3! = 10
Number of Combinations in which 4 at 1st place = 0 + 2 + 0 = 2
P(4 at 1st toss / Sum = 15) = 2/10 = 1/5

Comments

but the answer given is 1/18 :(

Answer 2

Using brute force

Number of combination in which sum is 15

3,6,6

4,5,6

4,6,5

5,5,5

5,4,6

5,6,4

6,3,6

6,4,5

6,5,4

6,6,3

Number of combination in which 4 at 1st place

4,5,6

4,6,5

p=2/10=1/5

Comments

Thanks . So 1/5 is correct we all are getting same

The answer given here is wrong then !