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In how many ways can 5 boys and 4 girls can be seated in a row so that they are in alternate position.
- a)2780
- b)2880
- c)2800
- d)2980
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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In how many ways can 5 boys and 4 girls can be seated in a row so that...
Answer – b) 2880 Explanation : First boys are seated in 5 position in 5! Ways, now remaining 4 places can be filled by 4 girls in 4! Ways, so number of ways = 5! 4! = 2880
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In how many ways can 5 boys and 4 girls can be seated in a row so that...
Problem: In how many ways can 5 boys and 4 girls can be seated in a row so that they are in alternate position.
Solution:
First, we need to select a position for the first boy. There are 5 choices for the first boy.
Next, we need to select a position for the first girl. There are 4 choices for the first girl.
Now, we need to alternate the remaining boys and girls in the available positions. There are 4 remaining boys and 3 remaining girls, so there are 4! ways to arrange the remaining boys and 3! ways to arrange the remaining girls.
Therefore, the total number of ways to arrange 5 boys and 4 girls in alternate positions is:
5 x 4 x 4! x 3! = 2880
Hence, the correct option is (B) 2880.
Solution:
First, we need to select a position for the first boy. There are 5 choices for the first boy.
Next, we need to select a position for the first girl. There are 4 choices for the first girl.
Now, we need to alternate the remaining boys and girls in the available positions. There are 4 remaining boys and 3 remaining girls, so there are 4! ways to arrange the remaining boys and 3! ways to arrange the remaining girls.
Therefore, the total number of ways to arrange 5 boys and 4 girls in alternate positions is:
5 x 4 x 4! x 3! = 2880
Hence, the correct option is (B) 2880.
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