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Class 11MathematicsPermutations and CombinationsCombinationsExpert
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From (6) red, (5) blue, and (4) green balls, (5) balls are to be selected with at least one ball of each color. How many selections are possible?

Answer and explanation

Correct answer: 2170

Since each colour must be represented among 5 balls, the only possible colour distributions are (3,1,1) and (2,2,1). For (3,1,1), the number of selections is \(\binom63\binom51\binom41+\binom61\binom53\binom41+\binom61\binom51\binom43=760\). For (2,2,1), it is \(\binom62\binom52\binom41+\binom62\binom51\binom42+\binom61\binom52\binom42=1410\). Hence, the total is \(760+1410=2170\). Option 1410 counts only the second distribution. Exam tip: when listing colour distributions, include every assignment of the quantities to the colours.

Related tags

CombinationsSelectionCounting PrinciplesCaseworkColour DistributionsPermutations And CombinationsMathematicsClass 11 Mcq
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