# Find n if nC8=nC12 - Mathematics and Statistics

Sum

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

#### Solution

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

If nCx = nCy, 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

Concept: Properties of Combinations
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.7 | Q 1 | Page 90