Question

Number of ways of selecting 5 letters from letters of word INDEPENDENT, is –

• A. 72
• B. 68
• C. 60
• D. 52

Answer 1

Answer: (A)

72

Answer 2

EEE, NNN, DD, I, P, T

Case-1 all 5 diff. ⁶C₅ = 6

Case-2 Alike, 3 diff. (⁴C₁ × 1) × ⁵C₃ = 30

Case-3 2Alike of I kind, 2Alike of 2^nd kind, 1 diff.

(³C₂ × 1 × 1) × ⁴C₁ = 12

Case-4 3 Alike, 2 diff. (²C₁ × 1) ⁵C₂ = 20

Case-5 3 Alike of 1 kind, 2 Alike of 2^nd kind

(²C₁ × 1 × ²C₁ × 1) = 4

Total = 6 + 30 + 12 + 20 + 4 = 72