Given 5 different green dyes, 4 different blue dyes and 3 different red dyes. The number of combinations of dyes can be chosen taking at least one green and one blue dye is

Out of 5 different green dyes, one or more can be chosen in $2^5-1=31$

Out of 4 different blue dyes, one or more can be chosen in $2^4-1=16$

Out of 3 different red dyes any number can be chosen in $2^3=8$

$\therefore$ The total number of combinations $=31\times 15\times 8=3720$