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Question

In how many ways can Rs. 16 be divided into 4 person when none of them get less than Rs. 3


A

70

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B

35

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C

64

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D

192

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Solution

The correct option is B

35


Required number of ways

= coefficient of x16 in (x3+x4+x5+.......x7)4

= coefficient of x16 in x12(1+x+x2+.......x4)4

= coefficient of x16 in x12(1x5)4(1x)4

= coefficient of x4 in (1x5)4(1x)4

= coefficient of x4 in (14x5+.....)

[1+4x+....+(r+1)(r+2)(r+3)3!x]

= (4+1)(4+2)(4+3)3! = 35

Aliter: Remaining 4 rupees can be distributed in 4+41C41 i.e., 35 ways


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