Question

In how many ways can 4 girls and 5 boys be arranged in a row so that all the four girls are together?

• A. 17280
• B. 720
• C. 2880
• D. 10000

Hint:

For grouping problems, consider groups as single units first and calculate arrangements accordingly.

Answer 1

The Correct Option is A

Consider the 4 girls as one unit (block).
Now, we have 5 boys + 1 girl block = 6 units to arrange: \[ 6! = 720 \] Inside the block, 4 girls can be arranged among themselves in: \[ 4! = 24 \] Total arrangements: \[ 6! \times 4! = 720 \times 24 = 17280 \] Thus, the correct answer is 17280.