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

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BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2087
Location: India
GPA: 3.12
3 identical red balls, 2 identical white balls, and 2 identical blue [#permalink]

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09 Nov 2017, 12:07
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Difficulty:

65% (hard)

Question Stats:

49% (00:55) correct 51% (01:57) wrong based on 37 sessions

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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
[Reveal] Spoiler: OA

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Stay hungry, Stay foolish

Math Expert
Joined: 02 Aug 2009
Posts: 5660
Re: 3 identical red balls, 2 identical white balls, and 2 identical blue [#permalink]

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09 Nov 2017, 18:29
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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 = $$\frac{6}{7*6*5}=\frac{1}{35}$$

D
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: 3 identical red balls, 2 identical white balls, and 2 identical blue   [#permalink] 09 Nov 2017, 18:29
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