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  4. If 8Cr-7C3= 7C2 , then r is equal to

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

UPSEEUPSEE 2008

Solution:

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