First slide

Permutations

Question

If $x \in N$ and $\frac{(2 x)!}{3! (2 x - 3)!} : \frac{x!}{2! (x - 2)} = 44 : 3,$ then $x$ is equal to

Moderate

A

6
B

7
C

11
D

12

Solution

$\frac{(2 x)!}{3! (2 x - 3)!} \cdot \frac{2! (x - 2)!}{x!} = \frac{44}{3}$
$\begin{array}{l} \Rightarrow \frac{(2 x) (2 x - 1) (2 x - 2)}{3 x (x - 1)} = \frac{44}{3} \\ \Rightarrow 2 x - 1 = 11 \Rightarrow x = 6 \end{array}$

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