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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 ______.
Options
3600
3720
3800
3600
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Solution
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 3720.
Explanation:
Possible number of choosing 5 different green dyes = 25
Possible number of choosing 4 blue dyes = 24
And possible number of choosing 3 red dyes = 23
If atleast one blue and one green dyes are selected then the total number of selection
= (25 – 1) × (24 – 1) × 23
= 31 × 15 × 8
= 3720
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