Question

If ³⁵C_n+7 = ³⁵C4_n–2 then find the value of n.

Answer 1

Given: ³⁵C_n+7 = ³⁵C4_n–2

Need to find: Value of n

We know,

One of the property of combination is: If ⁿC_r = ⁿC_t, then,

(i) r = t OR

(ii) r + t = n

Applying property

(i) we get,

⇒ n + 7 = 4n – 2

⇒ 3n = 9

⇒ n = 3

Applying property

(ii) we get,

⇒ n + 7 + 4n – 2 = 35

⇒ 5n = 30

⇒ n = 6

Therefore, the value of n is either 3 or 6.