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Grade 12Magical Mathematics[Interesting Approach]

sir,i need an answer to this question from permutations and combinations.the question is:-there are n distinct white balls and n distinct black balls.if the number of ways of arranging them in a row such that neighbouring balls are of different colours is 1152 then value of n?

akashkrishna

11 Years agoGrade 12

3 Answers

Akshay

11 Years ago

n=4,

suppose it starts with black ball. sequence will be BWBW......BWBW,
and if it starts with white ball, sequence will be WBWB.....WBWB.
so, there are two cases,
for each case, total will be = n! * n!, n! to permute the white balls and other n! to permute black balls.

so, 1152=2*n!*n!,

576=(n!)^2,

n!=24,
n=4

Vijay Mukati

11 Years ago

Definately, you will have to start with white or black (2 cases) and then repeat the order as WBWBWB or BWBWBW … and ways to arrange n white or black balls will be factorial(n). Therefore 2*factorial(n)² = 1152. Therefore n = 4.

manmath

10 Years ago

n=4, suppose it starts with black ball. sequence will be BWBW......BWBW, and if it starts with white ball, sequence will be WBWB.....WBWB. so, there are two cases, for each case, total will ...

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