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In how many ways can 5 identical black balls and 7 identical

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In how many ways can 5 identical black balls and 7 identical [#permalink] New post 22 Oct 2005, 09:49
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In how many ways can 5 identical black balls and 7 identical white balls be arranged in a row so that no 2 black balls are together

A)56
B)64
C)65
D) 316
E)560
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 [#permalink] New post 22 Oct 2005, 12:18
fresinha12 wrote:
8C3? or 8C5?

gsr wrote:
A) 8C3 = 56


8C3 = 8C5 :!:
Position of white balls is fixed. Since they are identical, number of ways to arrange them is 1.
We have 6 spaces in btw the white balls and 1 each to the left and right end to accomodate the black ball. So 8 places in total to arrange 5 balls
8C5 (or 8C3)
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 [#permalink] New post 23 Oct 2005, 08:24
there are 8 spaces availale so that no two black balls are together. that means 8! arrangements. but there are 5 identical black balls and 3 identical spaces. that`s why we have to divide by 5! and 3!. 8!/(5!3!).
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  [#permalink] 23 Oct 2005, 08:24
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