If 20 C r+1 = 20 C r–10 then find the value of 10 C r .

Question

Philoid · Accepted Answer

Given: ²⁰C_r+1 = ²⁰C_r–10 Need to find: Value of ¹⁰C_r We know, one of the property of combination is: If ⁿC_r = ⁿC_t, then, (i) r = t OR (ii) r + t = n We can’t apply the property (i) here. So we are going to use property (ii) ²⁰C_r+1 = ²⁰C_r–10 By the property (ii), ⇒ r + 1 + r – 10 = 20 ⇒ 2r = 29 ⇒ r = 14.5 We need to find out the value of ¹⁰C_r. But here r can’t be a rational number. Therefore the value of ¹⁰C_r can’t be find out.

If 20Cr+1 = 20Cr–10 then find the value of 10Cr.

If ²⁰C_r+1 = ²⁰C_r–10 then find the value of ¹⁰C_r.