Multiple choice

Two groups are to be formed from 10 boys such that the groups may or may not have the same size. How many ways can this be done?

  1. 255

  2. 511

  3. 1022

  4. 2024
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Each of the 10 boys can either be in group 1 or group 2. This gives 2^10 = 1024 total assignments. Excluding the cases where one group is empty (2 cases), we have 1022. Since the order of groups does not matter, we divide by 2, resulting in 511.

AI explanation

Assuming groups are named, each boy has 2 choices, which gives 2 to the power of 10, or 1024, total distributions. Excluding the 2 cases where a group gets zero boys, we are left with 1022 ways. If the two groups are identical and unnamed, we divide by 2 to avoid counting mirror-image divisions twice, which leaves 511 ways to form the groups.

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