The number of ways of distributing 3 identical physics books and 3 identical mathematics books among three students such that each student gets at least one book is 50 + K , where K is single digit nu

Question

The number of ways of distributing 3 identical physics books and 3 identical mathematics books among three students such that each student gets at least one book is 50 + K , where K is single digit number, then K is ____ .

TestHub · Accepted Answer

n ( A ) = 3 + 2 − 1 C 2 − 1 ​ × 3 + 2 − 1 C 2 − 1 ​ = 16 n ( B ) = n ( C ) = 16 n ( A ∩ B ) = 3 + 1 − 1 C 1 − 1 ​ 3 + 1 − 1 C 1 − 1 ​ = 1 = n ( B ∩ C ) = n ( C ∩ A ) n ( A ∩ B ∩ C ) = 0 Required no.of ways = 100 − ( 16 + 16 + 16 − 1 − 1 − 1 + 0 ) = 55 = 50 + 5 ∴ K = 5

Mathematics - Permutation & Combination Question with Solution | TestHub

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