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Find n if `""^"n""C"_8 = ""^"n""C"_12`

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#### Solution

`""^"n""C"_8 = ""^"n""C"_12`

If ^{n}C_{x} = ^{n}C_{y}, then either x = y or x = n − y

∴ 8 = 12 or 8 = n − 12

But 8 = 12 is not possible

∴ 8 = n – 12

∴ 8 + 12 = n

∴ 20 = n

∴ n = 20

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