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

Question

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

chetan2u · Accepted Answer

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

thinkvision · Answer

3/7 * 2/6 * 1/5 = 1/35 (D)

Robcastagna · Answer

Just out of my curiosity is this a 655 quant level question looks so easy since I would like to know if i can do the 655 questions in the quant section

Krunaal · Answer

The best way to know if you could do 655 level questions on the quant section is to do multiple sets of 605-655 level questions across topics and see if your accuracy on them is consistently more than 90 or 95%

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

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