There are 6 children at a family reunion, 3 boys and 3 girls. They will be lined up single-file for a photo, alternating genders. How man arrangements of the children are possible for this photo?
Which formula do I have to use for this question?
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Permutations/Combinations Question
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vineeshp
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Permutations.
_ _ _ _ _ _ - 6 places to fill. 1,3 and 5 to be filled by one gender and 2,4,6 to be filled by the other gender.
Treat the boys and girls as arranged separately.
The 3 boys can be arranged in 3! ways and girls too can be arranged in 3! ways.
And there are two ways of arranging the whole set.
i.e. BGBGBG and GBGBGB.
So 2 * 3! *3! ways.
My point is - Understand the concept and identify the way to go about it. Formulae will come to you naturally as you practice.
_ _ _ _ _ _ - 6 places to fill. 1,3 and 5 to be filled by one gender and 2,4,6 to be filled by the other gender.
Treat the boys and girls as arranged separately.
The 3 boys can be arranged in 3! ways and girls too can be arranged in 3! ways.
And there are two ways of arranging the whole set.
i.e. BGBGBG and GBGBGB.
So 2 * 3! *3! ways.
My point is - Understand the concept and identify the way to go about it. Formulae will come to you naturally as you practice.
Vineesh,
Just telling you what I know and think. I am not the expert.
Just telling you what I know and think. I am not the expert.
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vikram4689
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Already well explained, do ask in case you have doubts. This concept is tested frequently
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djiddish98
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I approached this problem in the following way by going over the number of options at each spot.
1st spot - 6 choices (any kid to start)
2nd spot - 3 choices (the 3 remaining from the gender not chosen)
3rd spot - 2 choices (the 2 remaining kids from the gender pool of the 1st spot)
4th spot - 2 choices ( the 2 remaining kids from the gender pool of the 2nd spot)
5th / 6th spot - the last kid in the gender pool for each
so we have 6 * 3 * 2 * 2 * 1 * 1
1st spot - 6 choices (any kid to start)
2nd spot - 3 choices (the 3 remaining from the gender not chosen)
3rd spot - 2 choices (the 2 remaining kids from the gender pool of the 1st spot)
4th spot - 2 choices ( the 2 remaining kids from the gender pool of the 2nd spot)
5th / 6th spot - the last kid in the gender pool for each
so we have 6 * 3 * 2 * 2 * 1 * 1
