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1. Write by hand, the formula for the counting rule of an experiment with k-steps with nk outcomes each. This is a process of randomly selecting k numbers (or objects) with replacement (or repetition). Look for the formula in your notes, PowerPoint slides or textbook.

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Answer:

         [tex]\large\boxed{\large\boxed{(n_k)^k}}[/tex]

Explanation:

The formula for the counting rule of an experiment with k-steps with [tex]n_k[/tex]outcomes each. This is a process of randomly selecting k numbers (or objects) with replacement (or repetition). Look for the formula in your notes, PowerPoint slides or textbook.

  • For the first step you have: [tex]n_k[/tex]  posibble outcomes

  • For the second step you have:  [tex]n_k[/tex]  posibble outcomes

  • For the third step you have:  [tex]n_k[/tex]  posibble outcomes

  • For the k-step you have:  [tex]n_k[/tex]  posibble outcomes

Thus,  a per the Fundamental Counting Principle or counting rule, the number of possible outcomes is:

           [tex]n_k\cdot n_k\cdot n_k\cdot ...\cdot n_k[/tex]

That is [tex]n_k[/tex] multiplied by itself k time, which is [tex]n_k[/tex] raised to power [tex]k[/tex].

      [tex](n_k)^k[/tex]

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