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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: 3133
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, 13:07
1
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Question Stats:

51% (00:59) correct 49% (01:49) wrong based on 45 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

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Joined: 02 Aug 2009
Posts: 6792
Re: 3 identical red balls, 2 identical white balls, and 2 identical blue  [#permalink]

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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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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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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