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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.
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.
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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+3−1C3−1=5C2 = 10 (n similar objects can be distributed to r distinct groups in n+t−1Cr−1 ways)
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+3−1C3−1=5C2 = 10 (n similar objects can be distributed to r distinct groups in n+t−1Cr−1 ways)
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