Question

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. 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.)

Answer 1

Total possible sequence is

Since, there are five places have exactly 1's

so, remaining =35-5=30

Number of possible sequence 30 other numbers is

Number of ways by which exactly five 1s placed in 35 places is

Total number of possible sequence of exactly five 1s is

now, we can find probability

now, we can simplify it

now, we can simplify it

and we get

..........Answer