The number of ways of arranging 11 objects A , B , C , D , E , F , α , α , α , β , β so that every β lie between two α (not necessarily adjacent) is K × 6 ! × 11 C 5 , then K is ____ .

Question

The number of ways of arranging 11 objects A , B , C , D , E , F , α , α , α , β , β so that every β lie between two α (not necessarily adjacent) is K × 6 ! × 11 C 5 ​ , then K is ____ .

TestHub · Accepted Answer

There are three major ways αα ββ α , α ββ αα and α β α β α Each major way has six empty spaces. The number of ways of putting letters at these empty spaces must be non-negative integer function of x 1 ​ + x 2 ​ + … + x 6 ​ = 6 = 6 + 6 − 1 C 6 − 1 ​ = 11 C 5 ​ No.of arrangements is = 3 × 11 C 5 ​ × 6 ! ⇒ K + 3

Mathematics - Permutation & Combination Question with Solution | TestHub

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