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In how many ways can 21 identical Red balls and 19 identical Blue ball
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02 Feb 2022, 06:39
02 Feb 2022, 06:39
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Question Stats:
33% (01:45) correct
66% (01:53) wrong based on 6 sessions
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In how many ways can 21 identical Red balls and 19 identical Blue balls be arranged in a row so that no 2 Blue balls are together?
A. \(\frac{22!}{3!19!}\)
B. \(\frac{2!}{19!22!}\)
C. \(\frac{21!}{2!19!}\)
D. \(\frac{19!}{3!22!}\)
E. \(\frac{21!}{3!19!}\)
A. \(\frac{22!}{3!19!}\)
B. \(\frac{2!}{19!22!}\)
C. \(\frac{21!}{2!19!}\)
D. \(\frac{19!}{3!22!}\)
E. \(\frac{21!}{3!19!}\)
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Re: In how many ways can 21 identical Red balls and 19 identical Blue ball
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02 Feb 2022, 06:57
02 Feb 2022, 06:57
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Carcass wrote:
In how many ways can 21 identical Red balls and 19 identical Blue balls be arranged in a row so that no 2 Blue balls are together?
A. \(\frac{22!}{3!19!}\)
B. \(\frac{2!}{19!22!}\)
C. \(\frac{21!}{2!19!}\)
D. \(\frac{19!}{3!22!}\)
E. \(\frac{21!}{3!19!}\)
A. \(\frac{22!}{3!19!}\)
B. \(\frac{2!}{19!22!}\)
C. \(\frac{21!}{2!19!}\)
D. \(\frac{19!}{3!22!}\)
E. \(\frac{21!}{3!19!}\)
sritamasia wrote:
In how many ways can 21 identical Red balls and 19 identical Blue balls be arranged in a row so that no 2 Blue balls are together?
A. \(\frac{22!}{3!19!}\)
B. \(\frac{2!}{19!22!}\)
C. \(\frac{21!}{2!19!}\)
D. \(\frac{19!}{3!22!}\)
E. \(\frac{21!}{3!19!}\)
A. \(\frac{22!}{3!19!}\)
B. \(\frac{2!}{19!22!}\)
C. \(\frac{21!}{2!19!}\)
D. \(\frac{19!}{3!22!}\)
E. \(\frac{21!}{3!19!}\)
Line up the 21 red balls in a row: RRRRRRRRRRRRRRRRRRR
Place a space on either side of each red ball: _R_R_R_R_R_R_R_R_R_R_R_R_R_R_R_R_R_R_R_R_R_
Important: Each available space is a potential location for a blue ball. This ensures that no two blue balls are together.
There are 22 spaces in total.
We'll select 19 of those 22 spaces and place a blue ball in each selected space.
So the question becomes, "In how many different ways can we select 19 spaces from 22 spaces?"
Since the order in which we select the 19 spaces does not matter, we can use combinations.
We can select 19 spaces from 22 spaces in 22C19 ways.
22C19 = 22!/(19!)(3!)
Answer: A
gmatclubot
Re: In how many ways can 21 identical Red balls and 19 identical Blue ball [#permalink]
02 Feb 2022, 06:57
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