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Class 11MathematicsPermutations and CombinationsCombinationsHard
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From (9) red and (8) blue balls (6) balls are to be selected with exactly (3) red balls. How many ways are there?

Answer and explanation

Correct answer: 4704

If exactly 3 red balls are selected, the remaining 3 of the 6 balls must be blue. The number of ways to choose 3 of the 9 red balls is \\(\binom{9}{3}=84\\), and to choose 3 of the 8 blue balls is \\(\binom{8}{3}=56\\). Therefore, the total number of selections is \\(\binom{9}{3}\binom{8}{3}=84\times56=4704\\). Option 2352 is only half of this product, so it is not correct. Exam tip: when fixed numbers are chosen from separate groups, multiply the corresponding combinations.

Related tags

CombinationsPermutations And CombinationsClass 11Selection PrincipleBinomial CoefficientsMathematicsClass 11 Mcq
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  6. 6A bag contains pens in 3 different colors, markers in 4 different colors, and pencils in 2 different colors. In how many ways can one pen, one marker, and one pencil be chosen?
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