Question

(n-1, 1) + (n - 1, 2)+ .....+ (n -1, n-1) = ______ ; n>1

(a) 2ⁿ-1 

(b) 2^n-2 

(c) 2^n-1-1 

(d) 2^n-1

Answer 1

Correct option: (c) 2^n-1-1

Explanation:

given: ^n–1c₁ + ^n–1c₂ + --- ^n–1c_n–1 

we know

ⁿc₀ + ⁿc₁ + ⁿc₂ + ⁿc₃ + ------ ⁿc_n = 2ⁿ 

Replacing n by(n – 1), we get

^n–1c₀ + ^n–1c₁ + ^n–1c₂ + ----- ^n–1c_n–1 = 2^n–1 

∴  ^n–1c₁ + ^n–1c₂ + ---- ^n–1c_n–1 = 2^n–1 – ^n–1c₀ 

= 2^n–1 – 1