Counting Techniques | MCQs

Explanation

The correct answer is: n!.

If X has n elements, then the number of permutations (i.e., arrangements) that can be taken on X is given by the factorial function:

n! = n × (n-1) × (n-2) × ... × 2 × 1

This counts the number of ways to arrange the n elements in a particular order.

Explanation

The word BOTSWANA has 8 letters, but it has two repeated letters (two S's and two A's).

To find the total number of words that can be formed, we need to divide the total number of permutations (8!) by the number of repetitions (2! for each pair of repeated letters).

So, the correct calculation is:

8! / (2! × 2!)

= 40320 / (2 × 2) = 40320 / 4 = 10080