If $C(n,2) : C(n,3) = 2 : 44 : 3$, then n is equal to

Question

There are 6 boys and 4 girls. Arrange their seating arrangement on a round table such that 2 boys and 1 girl can't sit together.

Answer 1

To find the value of $n$ such that $C(n,2) : C(n,3) = \frac{44}{3}$, we need to use the concept of combinations.

The formula for combinations is:

$C(n, r) = \frac{n!}{r!(n-r)!}$

First, calculate $C(n,2)$:

$C(n,2) = \frac{n(n-1)}{2}$

Now, calculate $C(n,3)$:

$C(n,3) = \frac{n(n-1)(n-2)}{6}$

$3n - 6 = 44$

$3n = 50$

$n = 6$

Hence, the correct value of $n$ is 6.

Correct Answer: $6$

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