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  4. If the number of ways in which 5 Apples, 5 Bananas, 5 Chickoos and 5 Oranges (fruits of the same species are alike) can be distributed equally among five persons so that exactly 2 of them get all 4 identical fruits and each of the remaining persons gets exactly 2 kind of fruits, is N then find the sum of the digits in N

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Q. If the number of ways in which 5 Apples, 5 Bananas, 5 Chickoos and 5 Oranges (fruits of the same species are alike) can be distributed equally among five persons so that exactly 2 of them get all 4 identical fruits and each of the remaining persons gets exactly 2 kind of fruits, is N then find the sum of the digits in N

Permutations and Combinations

Solution:

$(AAAAA) (BBBBB)(CCCCC)(OOOOO)$
$P _1, P _2, P _3, P _4, P _5 $
${ }^5 C _2 \times{ }^4 C _2 \times 2 ! \times{ }^3 C _2 \times 2 ! \times 2 !=1440$
$\therefore \text { sum of the digits }=9$