Multiple choice

A population consist of 8 members, a sub-group of 3 persons with replacement can be drawn in _____ ways.

  1. 512

  2. 256

  3. 128

  4. 64
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A Correct answer
Explanation

When drawing a sub-group of size k from a population of size n with replacement, each of the k positions has n choices. Thus, the total number of ways is n^k. Here, 8^3 = 512.

AI explanation

Because the selection is done with replacement, each of the 3 positions in the subgroup can be filled by any of the 8 members. By the multiplication principle, the total number of ways is 8 multiplied by 8 multiplied by 8, which equals 512.

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