nC8 = nC12 If nCx = nCy, then either x = y or x = n – y &there4; 8 = 12 or 8 = n – 12 But 8 = 12 is not possible &there4; 8 = n – 12 &there4; n = 20

English

Find n if nC8 = nC12

Find n if ⁿC₈ = ⁿC₁₂

Sum

ⁿC₈ = ⁿC₁₂

If ⁿC_x = ⁿC_y, then either x = y or x = n – y

∴ 8 = 12 or 8 = n – 12

But 8 = 12 is not possible

∴ 8 = n – 12

∴ n = 20

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Chapter 3: Permutations and Combination - Exercise 3.6 [Page 65]

Chapter 3 Permutations and Combination
Exercise 3.6 | Q 16. (i) | Page 65

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