Question

If $^{30}C_{r+2} = {^{30}C_{r-2}}$, then r equals :

• A. 8
• B. 15
• C. 30
• D. 32

Answer 1

Answer: (B)

15

Answer 2

Let $^{30}C_{r+2} = {^{30}C_{r-2}}$ ......(1) We know, If $^nC_{r_1} = {^{n}C_{r_2}}$ then $r_1 + r_2 = n$ In above given equation (1) we have $n = 30, r_1 = r + 2, r - 2 = r_2$ $\therefore \, r_1 + r_2 = r + 2 + r - 2 = 2r$ and $n = 30$ $\therefore \, 2r = 30 \, \Rightarrow \, r = 15$