If a die is rolled 30 times there are 630 different sequence

If a die is rolled 30 times, there are 630 different sequences possible. The following question asks how many of these sequences satisfy certain conditions. HINT [Use the decision algorithm discussed in Example 3 of Section 6.3.] What fraction of these sequences have exactly five 1s? (Round your answer to four decimal places.)

Solution

p = 1/6  is the probability to get a 1 when rolling a dice

by applying bernoulis theorem

p(x=5) = 5 * p⁵ * (1-p)^30-5  

= 5 * (1/6)⁵ * (1-1/6)²⁵

=  5 * (1/6)⁵ * (5/6)²⁵

⁼ 0.0000067