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Q.
If $^{30}C_{r+2} = {^{30}C_{r-2}}$, then r equals :
Permutations and Combinations
Solution:
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 $n = 30$
$\therefore \, 2r = 30 \, \Rightarrow \, r = 15$