WAEC - Further Mathematics (2022 - No. 18)
Evaluate \(4p_2 + 4C_2 - 4p_3\)
18
6
-6
-18
הֶסבֵּר
\(4p_2 + 4C_2 - 4p_3\)
\(np_r = \frac{n!}{[n-r]!} and nC_r = \frac{n!}{[n-r]!r!} \)
= \(\frac{4!}{[4-2]!} + \frac{4!}{[4-2]!2!} - \frac{4!}{[4-3]!} = \frac{4!}{2!} + \frac{4!}{2!2!} - \frac{4!}{1!}\)
= \(\frac{4*3*2!}{2!} + \frac{4*3*2!}{2!2!} - \frac{4*3*2*1}{1!}\)
12 + 6 - 24 = -6