A lift with 7 people stops at 10 floors. People varying from zero to 7 go out at each floor. The number of ways in which the lift can get emptied, assuming each way only differ by number of people leaving at each floor, is_______.

11440

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5005

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5720

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10010

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Solution

The correct option is A
11440

Let us take Ai number of persons gets out of lift at $i^{t h}$ floor.

$A_{1} + A_{2} + A_{3} + . . . . . . . . . A_{10} = 7$

This problem is similar to distributing 7 people among 10 floors.

It can be done = $^{7 + 10 - 1} C_{10 - 1}$ = $^{16} C_{9}$ = $^{16} C_{7}$

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A lift with 7 people stops at 10 floors. People varying from zero to 7 go out at each floor. The number of ways in which the lift can get emptied, assuming each way only differ by number of people leaving at each floor, is_______.

The correct option is A 11440 Let us take Ai number of persons gets out of lift at ith floor. A1+A2+A3+.........A10=7 This problem is similar to distributing 7 people among 10 floors. It can be done = 7+10−1C10−1 = 16C9 = 16C7