Question

Given five different green dyes, four different blue dyes and three different red dyes ; how many combinations of dyes can be chosen, taken at least at least one green and one blue dye ?

• A. $3600$
• B. $3720$
• C. $3780$
• D. $Noneoftheabove$

Answer 1

The correct option is B $3720$

Green dyes $=5$

Blue dyes $=4$

Red dyes $=3$

The number of ways of choosing of at least one green and one blue is $=(2^5-1)\times (2^4-1)\times 2^3$

$=(32-1)\times (16-1)\times 8$

$=31\times 15\times 8$

$=3720$