Question

How many unique ways are there to arrange the letters in the word PRIOR?

a) 60
b) 120
c) 30
d) 24

Answer 1

There are 60 unique ways to arrange the letters in the word PRIOR, accounting for the repeating 'R' letters using the permutation formula with identical items.

Step-by-step explanation:

To determine how many unique ways there are to arrange the letters in the word PRIOR, we need to account for the repeating 'R' letters. The formula for the number of permutations of n items with n1, n2, ..., nk identical items is:

n! / (n1! × n2! × ... × nk!) where '!' denotes factorial.

PRIOR consists of 5 letters where 'R' appears twice. Using the formula, the number of unique permutations is:

5! / (2!) = (5 × 4 × 3 × 2 × 1) / (2 × 1) = 120 / 2 = 60 unique arrangements.