If a die is rolled 30 times, there are 6^{30}

Keaton Good

Keaton Good

Answered question

2022-01-23

If a die is rolled 30 times, there are 630 different sequences possible.
What fraction of these sequences have exactly eight 1s and eight 6s?

Answer & Explanation

fumanchuecf

fumanchuecf

Beginner2022-01-24Added 21 answers

A die contains six possible outcomes, and the number of them when a die is rolled 30 times is 630
It would be 30 slots, when a die is rolled 30 times. The sequence must consist of eight 1's and eight 6's.
This can be done in 30C16 ways. These 16 slots can be filled in first eight 1's by 16C8 and remaining 8 slots can be filled in first eight 6's by 8C8. After all this filling there would be 14 remaining slots, which can be filled with numbers 2, 3, 4, 5 in 414
The vraction of 630 sequences that have eight 1's and eight 6's is
Probability=30C16×15C8×8C8×414630
=0.0023

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