If a die is rolled 30 times, there are 630 different sequences possible. The following...

Bobbie Comstock

Bobbie Comstock

Answered

2022-01-05

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.
What fraction of these sequences have exactly three 3s and three 2s?

Answer & Explanation

censoratojk

censoratojk

Expert

2022-01-06Added 46 answers

Think of a sequence as thirty empty slots.
We want to 10 slots to contain 3’s and 2’s of which we want three of the slots to be 3, the other slots to be 2. The other 20 slots can be containing any of 1, 4, 5, and 6.
As a fraction of the total of 630
Firstly, select 10 slots to house the 3's and 2's - C(30,6)
Now, select 5 slots for the 3's out of 10 chosen - (6,5)
Select remaining 5 slots - C(3,3)
Total=C(30,6)×C(6,5)×C(3,3)×420
C(30,6)×C(6,5)×C(3,3)×420630=0.01512 as a fraction of the total of 630

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