Question

Given five different green dyes, four different blue dyes and three different red dyes, the number of combinations of dyes which can be chosen taking atleast one green and one blue dye is

• A. 3600
• B. 3720
• C. 3800
• D. 3500

Answer 1

Answer: (B)

Possible number of ways of choosing 5 green dyes
$ =\square \square \square \square \square $
$ =2 \times 2 \times 2 \times 2 \times 2=2^5$
(dye can be selected or not selected)
Similarly, possible number of ways of choosing 4 blue dyes and 3 red dyes are $2^4$ and $2^3$ respectively.
Thus, possible number of ways of choosing atleast one green and one blue dye is $2^5-1$ and $2^4-1$
i.e., $31$ and $15$ .
Required number of ways $=31 \times 15 \times 2^3$
$=31 \times 120=3720$