First slide

Combinations

Question

Suppose $p \in N, n =^{P} C_{2} x$ and $m =^{n} C_{2}$ if $4 m : n =$ $18 : 1,$ then $p$ is equal to

Moderate

A

11
B

9
C

7
D

5

Solution

$\begin{array}{l} m = \frac{1}{2} n (n - 1) \Rightarrow \frac{4 m}{n} = 2 (n - 1) = p (p - 1) - 2 \\ ∴ 18 = p (p - 1) - 2 \Rightarrow p = 5 \end{array}$

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