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There are 15 members of the show choir. In how many different ways can you arrange any 8 members in the front row?

User Jermane
by
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1 Answer

5 votes

We have the following:

The first chair can be any of the 15.

For each of those ...

The second chair can be any of the 14.

For each of those ...

And so on until choosing 8 chairs

.

.

.

The eighth chair can be any of 8.

For each of those ...

Number of ways to fill the 8 chairs = (15 x 14 x 13 x 12 x 11 x 10 x 9 x 8) = 259,459,200

But in each group of 8 people you can sit on (8 x 7 x 6 x 5x 4 x 3 x 2 x 1) = 40,320 orders.

So each group of 40,320 people is represented 24 times out of 259,459,200

Therefore, the answer is:


(259459200)/(40320)=6435

6435 sets of 8 members, in any order.

User J Steven Perry
by
5.1k points
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