In how many ways can 4 girls and 5 boys be arranged in a row so that all the four girls are together?Choices:- 16236 16543 13456 17280
Question
In how many ways can 4 girls and 5 boys be arranged in a row so that all the four girls are together?
Choices:
- 16236
- 16543
- 13456
- 17280
Solution
To solve this problem, we first consider the 4 girls as a single entity. So, we have 6 entities to arrange, the 5 boys and the group of 4 girls.
Step 1: Arrange the 6 entities. This can be done in 6! (6 factorial) ways.
Step 2: Arrange the 4 girls within their group. This can be done in 4! (4 factorial) ways.
So, the total number of arrangements is 6! * 4! = 720 * 24 = 17280.
Therefore, the correct answer is 17280.
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