# Find n if 21C6n = 21C(n2+5) - Mathematics and Statistics

Sum

Find n if 21C6n = ""^21"C"_(("n"^2 + 5))

#### Solution

21C6n = ""^21"C"_(("n"^2 + 5))

If nCx = nCy, then either x = y or x = n – y

∴ 6n = n2 + 5 or 6n = 21 – (n2 + 5)

∴ n2 – 6n + 5 = 0 or 6n = 21 – n2 – 5

∴ n2 – 6n + 5 = 0 or n2 + 6n – 16 = 0

If n2 – 6n + 5 = 0 then (n – 1)(n – 5) = 0

∴ n = 1 or n = 5

If n = 5 then

n2 + 5 = 30 > 21

∴ n ≠ 5

∴ n = 1

If n2 + 6n – 16 = 0 then (n + 8)(n – 2) = 0

n = – 8 or n = 2

n ≠ – 8

∴ n = 2

Is there an error in this question or solution?

#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 3 Permutations and Combination
Exercise 3.6 | Q 16. (iii) | Page 65