Multiple choice

In how many different ways can 4 females and 5 males be arranged in a row so that the four females sit together?

  1. 17280

  2. 12560

  3. 16480

  4. 18560

  5. None of these
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A Correct answer
Explanation

Treat the 4 females as one block. There are 5 males + 1 block = 6 units to arrange in 6! ways. The 4 females can be arranged within their block in 4! ways. Total = 6! * 4! = 720 * 24 = 17280.

AI explanation

Treat the 4 females as a single block, which leaves you with 6 units to arrange in a row (the female block and the 5 males). These 6 units can be arranged in 6! ways, and the 4 females within their block can be arranged in 4! ways. By the fundamental principle of multiplication, the total arrangements are 6! times 4!, which is 720 times 24. This multiplication results in 17280. The result is 17280.

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