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In how many different ways can 3 boys and 3 girls be arranged in a row
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08 Aug 2023, 03:28
08 Aug 2023, 03:28
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50% (00:38) correct
50% (00:53) wrong based on 6 sessions
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In how many different ways can 3 boys and 3 girls be arranged in a row, such that boys and girls alternate?
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Re: In how many different ways can 3 boys and 3 girls be arranged in a row
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07 Oct 2023, 00:30
07 Oct 2023, 00:30
Expert Reply
We want an arrangement of 3 boys and 3 girls such that they sit in alternate manner.
The possible arrangement for which is:
𝐵 𝐺 𝐵 𝐺 𝐵 𝐺 or 𝐺 𝐵 𝐺 𝐵 𝐺 𝐵.
Let’s consider the first case (starting with boy).
BGBGBG: 3 boys can be arranged on 3 places, in a row in 3! Ways
(Using ‘𝑛’ things can be arranged on a straight line in 𝑛! ways)
Similarly, 3 girls can be arranged on 3 places in 3! ways.
So, total possible ways = 3! × 3! = 36
Similarly, considering the other case, when they start sitting with a girl,
GBGBGB, also has 3! × 3! = 36 ways.
Now, BGBGBG or GBGBGB is possible, so we will add the total number of possibilities in
both the cases.
Hence, Total ways = 36 + 36 = 72
Ans. (B)
The possible arrangement for which is:
𝐵 𝐺 𝐵 𝐺 𝐵 𝐺 or 𝐺 𝐵 𝐺 𝐵 𝐺 𝐵.
Let’s consider the first case (starting with boy).
BGBGBG: 3 boys can be arranged on 3 places, in a row in 3! Ways
(Using ‘𝑛’ things can be arranged on a straight line in 𝑛! ways)
Similarly, 3 girls can be arranged on 3 places in 3! ways.
So, total possible ways = 3! × 3! = 36
Similarly, considering the other case, when they start sitting with a girl,
GBGBGB, also has 3! × 3! = 36 ways.
Now, BGBGBG or GBGBGB is possible, so we will add the total number of possibilities in
both the cases.
Hence, Total ways = 36 + 36 = 72
Ans. (B)
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Re: In how many different ways can 3 boys and 3 girls be arranged in a row
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08 Oct 2023, 22:54
08 Oct 2023, 22:54
1
There are 3 boys and 3 girls. Hence,
3C1*3C1*2C1*2C1*1C1*1C1 = 3*3*2*2*1*1 = 72
3C1*3C1*2C1*2C1*1C1*1C1 = 3*3*2*2*1*1 = 72
