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3 identical red balls, 2 identical white balls, and 2 identical blue

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3 identical red balls, 2 identical white balls, and 2 identical blue  [#permalink]

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New post 09 Nov 2017, 13:07
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3 identical red balls, 2 identical white balls, and 2 identical blue balls are to be randomly arranged in a row.
What is the probability that the first three balls in the row are red balls?

A. \(\frac{1}{210}\)
B. \(\frac{1}{105}\)
C. \(\frac{1}{70}\)
D. \(\frac{1}{35}\)
E. \(\frac{4}{35}\)

Source: Experts Global

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Re: 3 identical red balls, 2 identical white balls, and 2 identical blue  [#permalink]

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New post 09 Nov 2017, 19:29
pushpitkc wrote:
3 identical red balls, 2 identical white balls, and 2 identical blue balls are to be randomly arranged in a row.
What is the probability that the first three balls in the row are red balls?

A. \(\frac{1}{210}\)
B. \(\frac{1}{105}\)
C. \(\frac{1}{70}\)
D. \(\frac{1}{35}\)
E. \(\frac{4}{35}\)

Source: Experts Global




7 balls are there and these can be arranged in 7! ways
but there are 3 identical red balls, 2 identical white balls, and 2 identical blue balls, so to remove repetitions = \(\frac{7!}{3!2!2!}=7*6*5\)

let first three be red, remaining 4 positions are to be filled by 2 identical white balls, and 2 identical blue balls = \(\frac{4!}{2!2!}=6\)

so probability = \(\frac{6}{7*6*5}=\frac{1}{35}\)

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Re: 3 identical red balls, 2 identical white balls, and 2 identical blue &nbs [#permalink] 09 Nov 2017, 19:29
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