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  • 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

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. 3600
[Hint: Possible numbers of choosing or not choosing 5 green dyes, 4 blue dyes and 3 red dyes are 2^5, 2^4 \text{and } 2^3, respectively.]

 

Answers (1)

The answer is the option (b).

At least one green dye can be chosen in ^5C_1+^5C_2+^5C_3+^5C_4+^5C_5=2^5-1ways 

  At least one blue dye can be chosen in ^4C_1+^4C_2+^4C_3+^4C_4=2^4-1ways 

 Any number of red dyes can be chosen in  ^3C_0+^3C_1+^3C_2+^3C_3=2^3ways 

 So, total number of selection=\left (2^5-1 \right )*\left (2^4-1 \right )*\left (2^3 \right )=3720

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infoexpert21

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