Question 12 of 42intermediate🔧 ApplyNumerical4 marks

Determine n if (i) ²ⁿC₃ : nC₃ = 12 : 1 (ii) ²ⁿC₃ : nC₃ = 11 : 1

(i)
Answer

n = 5

(ii)
Answer

n = 6

Explanation

This question tests the application of the combination formula nCr = n!/(r!(n-r)!). The key insight is that when comparing ratios of combinations, we can expand the factorial expressions and simplify algebraically. The context shows similar problem-solving approaches in Exercise 6.4 and Example 12, where factorial terms are expanded and equations are solved for n.