Multiple choice

A group has 8 members. The number of males and that of females are equal. In how many ways can they be arranged in a row of 8 seats to occupy alternate positions?

  1. 1002

  2. 1100

  3. 1000

  4. 1152

  5. 1120
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

8 members, 4 males, 4 females. Alternate positions: M F M F M F M F or F M F M F M F M. For each pattern, 4! ways to arrange males and 4! ways for females. Total = 2 * (4! * 4!) = 2 * (24 * 24) = 2 * 576 = 1152.

AI explanation

With 4 males and 4 females, they can occupy alternate positions in either an M-F-M-F-M-F-M-F pattern or an F-M-F-M-F-M-F-M pattern, giving 2 arrangements of gender patterns. The 4 males can be arranged in their seats in 4! ways and the 4 females can be arranged in their seats in 4! ways. The total number of arrangements is 2 times 4! times 4!, which equals 2 times 24 times 24 = 1152.

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