Question 23 of 42intermediate🔧 ApplyNumerical2 marks

If nC₈ = nC₂, find nC₂.

Correct Answer

nC₂ = 45

Exercise: EXERCISE 6.4 | Q: 1 | (Page 20)
For More Understanding

Explanation

This question tests the property that nC_a = nC_b implies either a = b or a = n - b. Since 8 ≠\neq 2, we must have 8 = n - 2, giving n = 10. Then applying the combination formula gives 10C₂ = 45.

Solution Steps

  1. Step 1: Given nC₈ = nC₂. Using the property nC_a = nC_b ⇒ a = b or a = n - b, we have either 8 = 2 or 8 = n - 2.

  2. Step 2: Since 8 ≠\neq 2, we get 8 = n - 2, therefore n = 10.

  3. Step 3: Now finding nC₂ = ¹⁰C₂ = 10!/(2! × 8!) = (10×910 \times 9 × 8!)/(2×12 \times 1 × 8!) = 90/2 = 45.

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