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. $3500$

Answer 1

Answer: (B)

$3720$

No. of ways by which at least $1$ green dye from $5$ different green dyes$=2^5-1$

No. of ways by which at least $1$ blue dye from $4$ different blue dyes$=2^4-1$

$3$ different green dye can be chosen in $2^3$ ways

So, required ways$=(2^5-1)(2^4-1)\left(2^3\right)=33\times 15\times 8=3720$