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!

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 _________________ Manhattan Review Locations: Manhattan Review Dilsukhnagar | GMAT Prep Begumpet | GRE Prep Visakhapatnam | Warangal GRE Coaching | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

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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