#combinations and permutations

24 messages · Page 1 of 1 (latest)

barren yacht
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  1. A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has

(iii) At least three girls?

total number of ways the team can have
at least three girls = 4C3 × 7C2 + 4C4 × 7C1 = 4 × 21 + 7= 84 + 7= 91

In this case, it is getting all possibilities
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  1. A bag contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the bag, if at least one black ball is to be included in the draw?

What about here? The solution I could find is to first get the combination with at least 3 black ball and subtract from the combination

9C3 - 6C3

I don’t know if the number 9 question has the correct solution, but they both have the same question (get at least n balls/girls) How come the 2 same question have different ways? Am I missing something?

fiery elbowBOT
scenic lake
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Is this a repost?

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Oh well

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The difference is that you can distinguish two girls from each other

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But not two balls of the same color

barren yacht
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4 girls and 3 black balls is the same?

scenic lake
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A team formed with Anna (F) and James (M) is different from a team of Donna(F) and James (M)

However, a draw with 1 black ball and 2 white balls remains the same even if you swap out the black ball with another black ball

barren yacht
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Ohh I see, it's just logic. So if distinguishable then get all cases else if not like (3 roses, 5 chocolate cake) then just get the combination with those subtracted to without?

rose salmon
# barren yacht 8. A group consists of 4 girls and 7 boys. In how many ways can a team of 5 memb...

number 9 is at least 1 which also mean a black ball should exist, so you can just subract the cases where there are no black balls at all from the total ways

number 8 is at least 3, not 1, so it doesn't simply mean that a girl should exist, but 3 girls should exist, like even if there are already 1 or 2 girls it'll not be included since it's less than 3
well you can still actually solve it like number 9's way by subtracting the cases where there are less than 3 girls from the total ways, but you'll need to calculate more cases for when there're no girls, 1 girl, and 2 girls, which is longer
but if you did like the way above, you only need to calculate cases when there're 3 girls and 4 girls
no matter which way you choose, you cannot do it directly like number 9 since it's at least 3, which is greater than 1

rose salmon
barren yacht
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Oh right, I did not notice that the num 8 ask for exact number therefore I have to get all case while 9 only ask if it exist so subtracting it is the easiest way ( correct me if I'm wrong)

rose salmon
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btw it should be 6C3 not 6C8

barren yacht
barren yacht
rose salmon
rose salmon
barren yacht
rose salmon
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urwelcome

barren yacht
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@rose salmon While making a note, I realized the reason why it needed to be subtracted. First is the combination of everything (the combination that includes balls with black is included). then a combination of everything except black, so by subtracting it, it removes all combinations that do not include any black.

rose salmon
rose salmon
barren yacht