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Question

How many ways can Adarsh distribute 17 identical apples among 6 students if he can also keep some apples for himself and each student should get at least one apple and not more than 6? 



A

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B

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C

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D

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Solution

The correct option is D


Let x1,x2,x3,x4,x5,x6 be the number of apples adarsh can distribute.

The sum is less than or equal to 17.

x1+x2+x3+x4+x5+x6 17

Since adarsh can also keep some apples for himself introducing a dummy variable x7(x70)

inequality becomes an equation

x1+x2+x3+x4+x5+x6+x7=17

Here 1x1,x2,x3,x4,x5,x66 and x70

Number of solution = Coefficient of x17 in (x+x2+x3+.........x6)6(1+x+x2+x3+............)

Coefficient of x11 in (1x6)6(1x)7

Coefficient of x11 in (16x6)(1x)7

Coefficient of x11 in (16x6)(1+7C1x+8C2x2+9C3x3+..............) = 17C11611C6=17C6611C5


Mathematics

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