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Question

What are the numbers of ways in which 5 similar balls can be put in 4 distinct baskets when second basket has exactly two balls.



A

12

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B

10

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C

16

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D

18

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Solution

The correct option is B

10


Let's number of baskets as A, B, C and D

With the first constraint, 2 of balls are going to basket 2(B),

hence we have to(5-2) = 3 balls left to distribute among the remaining baskets.

So,

A + C + D = 3

Number of possible distributions = 3+31C31=5C2  = 10 (n similar objects can be distributed to r distinct groups in n+t1Cr1 ways)


Mathematics

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