Question

question from permutations and combinations​

Answer 1

Step-by-step explanation:

The value of 8C3 is 56

The value of 9C4 is 126

(n+2)C4 can be written as

$\frac{(n + 2)(n + 1)n(n - 1)}{1 \times 2 \times 3 \times 4}$

So substitute three values,

$56 + \frac{(n + 2)(n + 1)n(n - 1)}{24} = 126$

$\frac{(n + 2)(n + 1)n(n - 1)}{1 \times 2 \times 3 \times 4} = 126 - 56 = 70$

$(n + 2)(n + 1)n(n - 1) = 1680$

(n+2)(n+1)n(n-1) = 8 × 7 × 6 × 5

By comparing the both sides,

n + 2 = 8

n + 1 = 7

n = 6

n - 1 = 5

So n = 6

Option (a)

Cheers