Q. If $^{8} C_{r} -^{7} C_{3} =^{7} C_{2}$ , then $r$ is equal to

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A

3

B

4

C

8

D

6

Solution:

$^{8} C_{r} =^{7} C_{3} +^{7} C_{2}$
$\Rightarrow^{8} C_{r} =^{8} C_{3} (∵^{n} C_{r} +^{n} C_{r - 1} =^{n + 1} C_{r})$
$\Rightarrow r = 3$