Question

Given 5 different green dyes, four different blue dyes and three different red dyes, the number of combinations of dyes which can be chosen taking at least one green and one blue dye is
(a) 3600
(b) 3720
(c) 3800
(d) 3600

Answer 1

Number of ways of selecting one green dye is ⁵C₁ + ⁵C₂ + ⁵C₃ + ⁵C₄ + ⁵C₅ = 2⁵⁻¹ ways.
Number of ways of selecting one blue dye can be choosen is ⁴C₁ + ⁴C₂ + ⁴C₃ + ⁴C₄ = 2⁴⁻¹ ways.
and
Number of ways of selecting red dye can be choosen in ³C₀ + ³C₁ + ³C₂ + ³C₃ = 2³ ways.
So, total number of required selection
= (2⁵ − 1) × (2⁴−1) × 2³
= 3720
Hence, the correct answer is option B.