Question 64542: Balls numbered 1 to 12 are dropped from the top of a maze, flow thru and land in slot A, B, C and D. In how many ways can the ball land if a)5,3,1,3 balls fall into A, B, C and D b)an equal number of balls fall into each slot and c) two slots are empty and an equal number of balls fall into the other two slots?
I think that part a) 12!/5!3!1!3! and b) 12!/4.3! are these ok? please help with part c.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Balls numbered 1 to 12 are dropped from the top of a maze, flow thru and land in slot A, B, C and D. In how many ways can the ball land if a)5,3,1,3 balls fall into A, B, C and D b)an equal number of balls fall into each slot and c) two slots are empty and an equal number of balls fall into the other two slots?
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a)Pick 5 balls from the 12 in 12C5 =792 ways
..Pick 3 balls from the 7 remaining in 7C3=35 ways
..Pick 1 ball from the 4 remaining in 4C1=4 ways
..Pick 3 balls from the 3 remaining in 3C3=1 way
Total # of ways to get 5,3,1,3 = 792*35*4*1=110880 ways
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b)12C3*9C3*6C3*3C3=369600ways
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12C6 ways to put 6 in one slot
6C6=1 way to put 6 in another slot
4C2 ways to pick the two slots that will contain the balls
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Cheers,
Stan H.
Stan H.
c)12C6*6C6=5544 ways
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