Evaluate \(4p_2 + 4C_2 - 4p_3\)
FURTHER MATHEMATICS
WAEC 2022
Evaluate \(4p_2 + 4C_2 - 4p_3\)
- A. 18
- B. 6
- C. -6
- D. -18
Correct Answer: C. -6
Explanation
\(4p_2 + 4C_2 - 4p_3\)
\(np_r = \frac{n!}{[n-r]!} and nC_r = \frac{n!}{[n-r]!r!} \)
= \(\frac{4!}{[4-2]!} + \frac{4!}{[4-2]!2!} - \frac{4!}{[4-3]!} = \frac{4!}{2!} + \frac{4!}{2!2!} - \frac{4!}{1!}\)
= \(\frac{4*3*2!}{2!} + \frac{4*3*2!}{2!2!} - \frac{4*3*2*1}{1!}\)
12 + 6 - 24 = -6
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