Question

If ¹P₁ + 2. ²p₂ + 3. ³p₃ + ....... 15. ¹⁵P₁₅ = ^qP_r – s, 0 ≤ s ≤ 1, then ^q+sC_r–s is equal to ______.

पर्याय

• 135

• 136

• 137

• 138

Answer 1

If ¹P₁ + 2. ²p₂ + 3. ³p₃ + ....... 15. ¹⁵P₁₅ = ^qP_r – s, 0 ≤ s ≤ 1, then ^q+sC_r–s is equal to 136.

Explanation:

¹P₁ + 2. ²p₂ + 3. ³p₃ + ....... 15. ¹⁵P₁₅

= 1! + 2.2! + 3.3! + .... + 15.15!

= 1! + ((3 – 1)2!) + ((4 – 1)3!) + ((16 – 1)15!)

= 1! + 3! – 2! + 4! – 3! + 5! – 4! + .... + 16! – 15!

= 16! + 1 – 2!

= 16! – 1! = ^qP_r – s

⇒ q = r = 16 and s = 1

So, ^q+sC_r–s = ¹⁷C₁₅ = `(17 xx 16)/2` = 136