If nCr+1 = nC8 then find the value of 22Cn.

1.	If nCr+1 = nC8 then find the value of 22Cn.
Answer» Given: ⁿC_r+1 = ⁿC₈ Need to find: Value of ²²C_n We know, One of the property of combination is: If ⁿC_r = ⁿC_t, then, (i) r = t OR (ii) r + t = n We are going to use property (i) ⁿC_r+1 = ⁿC₈ By the property (i), ⇒ r + 1 = 8 ⇒ r = 7 Now we are going to use property (ii) ⇒ n = 8 + 7 + 1 = 16 Therefore, ²²C_n = ²²C₁₆ = 74613.

Answer»

Given: ⁿC_r+1 = ⁿC₈

Need to find: Value of ²²C_n

We know,

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

(i) r = t OR

(ii) r + t = n We are going to use property

(i) ⁿC_r+1 = ⁿC₈ By the property (i),

⇒ r + 1 = 8

⇒ r = 7 Now we are going to use property

(ii) ⇒ n = 8 + 7 + 1 = 16

Therefore,

²²C_n = ²²C₁₆ = 74613.

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