If a die is rolled 35 times there are 635 different sequence

If a die is rolled 35 times, there are 6³⁵ different sequences possible. The following question asks how many of these sequences satisfy certain conditions.

What fraction of these sequences have exactly five 1s? (Round your answer to four decimal places.)

Solution

die is rolled 35 times,

so n=35

prob of 1, p= 1/6

prob. of non-one, q= 5/6

x:number of 1

P(x=5) = p^5 * q^30

P(x=5) = (1/6)^5 * (5/6)^30

P(x=5) = 5.42 * 10^(-7)