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

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

Tardigrade Admin · Accepted Answer

Possible number of ways of choosing 5 green dyes

= □□□□□

= 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

Q. 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

3600

3720

3800

3500