The number of ways of distributing 15 identical balloons, 6 identical pencils and 3 identical erasers among 3 children, such that each child gets at least four balloons and one pencil, is
Explanation:
We know that number of distributing n identical objects amongst r different groups = n+r-1Cr-1
Distributing balloons Since each child gets at least 4 balloons, we will first give 4 balloons to each of the 3 children. Now we have 3 identical balloons to be distributed to 3 children. Number of ways of doing this = 3+3-1C3-1 = 10 ways
Distributing pencils Since each child gets at least 1 pencil, we will first give 1 pencil to each of the 3 children. Now we have 3 identical pencils to be distributed to 3 children. Number of ways of doing this = 3+3-1C3-1 = 10 ways
Distributing erasers We have 3 identical erasers to be distributed to 3 children. Number of ways of doing this = 3+3-1C3-1 = 10 ways
∴ Total number of ways = 10 × 10 × 10 = 1000
Hence, 1000.
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