Multiple choice

An arrangement has to be made so that '2n' boys and 'n' girls stand in a row such that no two girls stand together. What minimum value of 'n' can give at least 151,200 choices to make this arrangement?

  1. 2

  2. 3

  3. 4

  4. 6

  5. 7
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The number of ways to arrange 2n boys and n girls such that no two girls are together is (2n)! * P(2n+1, n). For n=3, 6 boys and 3 girls: 6! * P(7, 3) = 720 * (7*6*5) = 720 * 210 = 151,200. This matches the requirement.

AI explanation

To ensure no two girls stand together, we first arrange the 2n boys in a row, which can be done in (2n)! ways. This arrangement creates (2n + 1) gaps, and we place the n girls into these gaps, which gives (2n + 1)Pn choices. Substituting n = 3 gives 6! multiplied by 7P3, which equals 720 multiplied by 210 for a total of 151,200 choices, so the minimum value is 3.

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