Evaluate n 1Cn-2 If n 15 - JAMB Mathematics 2012 Question
Evaluate n+1Cn-2 If n =15
A
3630
B
3360
C
1120
D
560
correct option: d
\(\frac{n + 1 (n - 2)}{(n + 1)!}\)
\(\frac{(n + 1) + (n - 2)!(n - 2)!}{(n + 1)!}\)
\(\frac{(n + 1)(n + 1 -1)(n+1-2)(n+1-3)!}{3!(n-2)!}\)
\(\frac{(n + 1)(n)(n-1)(n-2)!}{3!(n-2)!}\)
\(\frac{(n + 1)(n)(n-1)}{3!}\)
Since n = 15
\(\frac{(15 + 1)(15)(15-1)}{3!}\)
\(\frac{16 \times 15 \times 14}{3 \times 2 \times 1}\)
= 560
\(\frac{(n + 1) + (n - 2)!(n - 2)!}{(n + 1)!}\)
\(\frac{(n + 1)(n + 1 -1)(n+1-2)(n+1-3)!}{3!(n-2)!}\)
\(\frac{(n + 1)(n)(n-1)(n-2)!}{3!(n-2)!}\)
\(\frac{(n + 1)(n)(n-1)}{3!}\)
Since n = 15
\(\frac{(15 + 1)(15)(15-1)}{3!}\)
\(\frac{16 \times 15 \times 14}{3 \times 2 \times 1}\)
= 560
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