Multiple choice

In how many ways can 4 boys and 4 girls be arranged in a row such that boys and girls alternate their positions (that is, boy girl)?

  1. 1032

  2. 1152

  3. 1254

  4. 1432

  5. 1564
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To alternate, the arrangement must be BGBGBGBG or GBGBGBGB. For each, there are 4! ways to arrange boys and 4! ways to arrange girls. Total = 2 * (4! * 4!) = 2 * (24 * 24) = 2 * 576 = 1152.

AI explanation

Since boys and girls must alternate, the 4 boys and 4 girls can be arranged in either a B G B G... pattern or a G B G B... pattern, giving 2 overall choices. The 4 boys can be arranged in their 4 spots in 4! ways, and the 4 girls can be arranged in their spots in 4! ways. The total arrangements equal 2 multiplied by 4! multiplied by 4!, which is 2 times 24 times 24. The result is 1152.

Keep practicing — related questions