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Question

In how many ways can 15 identical blankets be distributed among 6 persons such that everyone gets atleast one blanket and two particular persons get equal blankets and another three particular persons get equal blankets.

A
8
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B
15
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C
10
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D
12
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Solution

The correct option is D 12
The number of required ways of distributing blankets is equal to the number of solutions of the equation
3a+2b+c=15 (a,b,c1)
= coeff. of t15 in (t3+t6+t9+t12)×(t2+t4+...)(t+t2+...)
= coeff. of t9 in (1+t3+t6+t9)×(1+t2+t4+t6+t8)(1+t+t2++t9)
( neglecting higher powers )
= coeff. of t9 in (1+t2+t3+t4+t5+2t6+t7+2t8+2t9)(1+t+t2+..+t9)
=1+1+1+1+1+2+1+2+2
=12

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