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permutation/combination

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permutation/combination

by vaibhav101 » Sat Sep 01, 2018 5:48 am

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in how many ways can 17 people be seated around 2 round tables with seating capacities of 8 and 9 people?

A 17!/8!
B 7!*8!
C 17C9*7!*8!
D 9!
E 17C8*6!*7!
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by Jay@ManhattanReview » Sun Sep 02, 2018 10:41 pm
vaibhav101 wrote:In how many ways can 17 people be seated around 2 round tables with seating capacities of 8 and 9 people?

A 17!/8!
B 7!*8!
C 17C9*7!*8!
D 9!
E 17C8*6!*7!
Note that n objects can be arranged around a circle in (n−1)! ways

Let us first choose any 8 people to sit on the first table; the number of ways = 17C8 ways.

The selected 8 people can be seated in (8 − 1)! = 7! ways on the first table

The remaining 9 people can be seated in (9 − 1)! = 8! ways on the second table

Hence, the total number of ways: = 17C8×7!×9!

We do not see any such option as 17C8×7!×9!. However, we can modify 17C8. Note that nCr = nC(n-r); thus, 17C8 = 17C(17 - 8) = 17C9.

Thus, the total number of ways: = 17C9×7!×9!

The correct answer: C

Hope this helps!

-Jay
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by Scott@TargetTestPrep » Fri Sep 07, 2018 4:23 pm
vaibhav101 wrote:in how many ways can 17 people be seated around 2 round tables with seating capacities of 8 and 9 people?

A 17!/8!
B 7!*8!
C 17C9*7!*8!
D 9!
E 17C8*6!*7!
There are 17C8 or 17C9 (notice that 17C8 = 17C9) ways to divide the 17 people into a group of 8 people and another group of 9 people. In the group of 8 people, there are 7! seating arrangements in their round table (recall that a circular arrangement of n people is (n - 1)!). Similarly, in the group of 9 people, there are 8! sitting arrangement in their round table. Therefore, there are a total of

17C8 x 7! x 8! or 17C9 x 7! x 8!

seating arrangements possible.

Answer: C

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