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Distribute 30 different mangoes (i) equa...

Distribute 30 different mangoes (i) equally in 6 baskets and (ii) equally among 6 children.

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(i) Each basket contain 5 mangoes hence the number of distributions required `=((30)!)/(6!(5!)^(6))`, here order of basket is not important.

(ii) The case of distribution among children is different from that among basket since we do not make distinction on the choice of baskets, but we distinguish one child from every other child. We see that
`2^(nd)` child gets 5 mangoes out of 30 in `""^(30)C_(5)` ways
`3^(rd)` child gets 5 mangoes out of 20 in `""^(20)C_(5)` ways
`4^(th)` child gets 5 mangoes out of 15 in `""^(15)C_(5)` ways
`5^(th)` child gets 5 mangoes out of 10 in `""^(10)C_(5)` ways
`6^(th)` child gets 5 mangoes out of 5 in `""^(5)C_(5)` ways
`therefore ` Required no. of ways `=""^(30)C_(5).""^(25)C_(5).^(15)C_(5).^(10)C_(5).^(5)C_(5)=(30!)/((5!)^(6))`
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