JEE Main 2021 · Mathematics · Probability · hard

Three fair dice are thrown. If p is the probability that the sum of the numbers is 10, then 216 p equals

Numerical answer

Three fair dice are thrown. If

p

is the probability that the sum of the numbers is

10

, then

216\,p

equals

Show answer and solution

Answer: 27

Count ordered triples

(a,b,c)

with each from

1

6

and sum

10

. By enumeration the compositions are

(1,3,6)

and permutations:

6

(1,4,5)

6

(2,2,6)

3

(2,3,5)

6

(2,4,4)

3

(3,3,4)

3

. Total

27

, so

p=\tfrac{27}{216}

and

216p=27

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