If $^{8} C_{r} -^{7} C_{3} =^{7} C_{2}$ , find r.

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Solution

$^{8} C_{r} -^{7} C_{3} =^{7} C_{2}$

or $^{8} C_{r} =^{7} C_{3} +^{7} C_{2} =^{8} C_{3} =^{8} C_{5}$

$∴$ r = 3 or 5

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