Question

The value of (21C1 - 10C1) + (21C2 - 10C2) + (21C3 - 10C3) + (21C4 - 10C4) +...+ (21C10 - 10C10) is

Answer 1

Answer:

2 ^20 - 2 ^10

Step-by-step explanation:

Given The value of (21C1 - 10C1) + (21C2 - 10C2) + (21C3 - 10C3) + (21C4 - 10C4) +...+ (21C10 - 10C10) is

We know that (1 + x) ^n = n C₀ + n C₁ x + n C₂ x²------------n C ₙ x ⁿ  

We can write as

(21 C₀ + 21 C₁ ---------21 C₁₀) -  (10 C₀ + 10 C₁ +---------10 C₁₀) ( n C₀ = 1)

So We get n C ₙ  = 2 ⁿ

Since we have 11 terms and 11 x 2 = 22

So 2²¹ / 2 - 2¹⁰ = 2²¹⁻¹ - 2¹⁰

 = 2²⁰ - 2¹⁰