First slide

Permutations

Question

There are n distinct white and n distinct black balls. If the number of ways of arranging them in a row so that neighbouring balls are of different colors is 1152, then value of n is

Moderate

Solution

Number of arrangements are $2 n! n!$
Given that $2 n! n! = 1152$
or $(n!)^{2} = 576$
or $n! = 24$
or $n = 4$

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