Given 5 different green toys, 4 different blue toys and 3 different red toys, how many combinations of toys can be chosen taking at least one green and one blue toy?

Step-by-step solution

Selecting atleast 1 green toy out of 5 can be done in ^5 C ₁+ ^5 C ₂+ ^5 C ₃+ ^5 C ₄+ ^5 C ₅+=31 ways. Selecting atleast 1 blue toy out of 4 can be done in ^4 C ₁+ ^4 C ₂+ ^4 C ₃+ ^4 C ₄=15 ways. Selecting red toys without restriction can be done in ^3 C ₀+ ^3 C ₁+ ^3 C ₂+ ^3 C ₃=8 ways. Total number of ways =31 15 8