In how many number of ways can 4 men be arranged in 12 seats such that no two men sit side by side?

Question

Riddhish Bhalodia · Answer

This is bit difficult to explain in writing, but here goes

Let separate the 4 chairs required for people and hence we are left with 8 chairs

| _ | _ | _ | _ | _ | _ | _ | _ |

IN the diagram the dashes are the chairs and the verticle lines are the place where the 4 men who wants to sit separately can put their chairs
Hence it’s
$\binom{9}{4} \times 4!$
Answer = 3024

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In how many number of ways can 4 men be arranged in 12 seats such that no two men sit side by side?

In how many number of ways can 4 men be arranged in 12 seats such that no two men sit side by side?

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In how many number of ways can 4 men be arranged in 12 seats such that no two men sit side by side?

In how many number of ways can 4 men be arranged in 12 seats such that no two men sit side by side?

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