Question

Given 6 different toys of green colour, 5 different toys of blue colour and 4 different toys of red colour. Combination of toys that can be chosen taking at least one green and one blue toys are

(A)  31258

(B)  31248 

(C)  31

(D)  63

Answer 1

Correct option  (B) 31248

At least one green toy can be selected out of 6 different toys in

⁶C₁ +  ⁶C₂ + ..... + ⁶C₆ = 63  ways

After selecting one or more green toys we can select at least one blue toy out of 5 different blue toys in

⁵C₁ + ⁵C₁ + .... +  ⁵C₅ = 31 ways

After selecting at least one green toy and one blue toy, selection of red toys (no restriction) can be made in 

⁴C₀ + ⁴C₁ + .... +  ⁴C₄ = 16 ways

Therefore, the total number of selections = 63 x 31 x 16 = 31248.