Write the value of (5C1 + 5C2 + 5C3 + 5C4 + 5C5).

⇒ 5C1 + 5C2 + 5C3 + 5C4 + 5C5 ⇒ 6C2 + 6C4 + 1 [As 5C5 = 1] ⇒ 15 + 15 + 1 ⇒ 31

Q7 of 68 Page 347

Write the value of (⁵C₁ + ⁵C₂ + ⁵C₃ + ⁵C₄ + ⁵C₅).

⇒ ⁵C₁ + ⁵C₂ + ⁵C₃ + ⁵C₄ + ⁵C₅ ⇒ ⁶C₂ + ⁶C₄ + 1 [As ⁵C₅ = 1] ⇒ 15 + 15 + 1 ⇒ 31

Find the values of (i) ²⁰⁰C₁₉₈, (ii) ⁷⁶C₀, (iii) ¹⁵C₁₅.

If ^mC₁ = ⁿC₂ prove that m = n(n – 1).

If ⁿ⁺¹C₃ = 2(ⁿC₂), find the value of n.

If ⁿP_r = 720 and ⁿC_r = 120 then find the value of r.