Question

determine whether the following problem involves a permutation or combination. (it is not necessary to solve the problem.)
how many different 5 - letter passwords can be formed from the letters h, i, j, k, l, m, and n if no repetition of letters is allowed?

the problem involves a ▼ because the ▼ of letters selected ▼ matter.

Explanation:

Step1: Recall Permutation vs Combination

Permutation: order of selection matters. Combination: order does not matter.

Step2: Analyze the Problem

We are forming passwords (sequences of letters). The order of letters in a password (e.g., H I J vs I H J) creates different passwords, so order matters.

Step3: Determine the Type

Since order of letters (selection) matters, it's a permutation.

Answer:

The problem involves a \(\boldsymbol{\text{permutation}}\) because the \(\boldsymbol{\text{order}}\) of letters selected \(\boldsymbol{\text{does}}\) matter.