Question

If nc8 = nc2 find the value of n

Answer 1

Step-by-step explanation:

$\binom{n}{8} = \binom{n}{2} \\ \\ \frac{nf}{(n - 8)f \times 8f} = \frac{nf}{(n - 2)f \times 2f} \\ \\ nf \: \: cut \: \: from \: both \: \: side \\ \\ (n - 2)f \times 2f = (n - 8)f \times 8f \\ \\ (n - 2)f \times 2 = (n - 8)f \times 8 \times 7 \times6 \times 5 \times 4 \times 3 \times 2 \\ \\ (n - 2)f = (n - 8)f \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \\ \\ (n -2 )(n - 3)(n - 4)(n - 5)(n - 6)(n - 7)(n - 8)f = (n - 8)f \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \\ \\ (n - 2)(n - 3)(n - 4)(n - 5)(n - 6)(n - 7) = 8 \times 7 \times 6 \times 5 \times 4 \times 3$