Reading Time: < 1 minute
Last Updated on May 11, 2023
GMAT OFFICIAL GUIDE PS
Solution:
This is a permutation problem, because the order of the letters matters. Let’s first determine how many ways we can arrange the letters. Since there are 2 repeating I’s, we can arrange the letters in 5!/2! = 120/2 = 60 ways.
We also have the following equation:
60 = (number of ways to arrange the letters with the I’s together) + (number of ways without the I’s together).
Let’s determine the number of ways to arrange the letters with the I’s together.
We have: [I-I] [D] [G] [T]
We see that with the I’s together, we have 4! = 24 ways to arrange the letters.
Thus, the number of ways to arrange the letters without the I’s together (i.e., with the I’s separated) is 60 – 24 = 36.
Answer: D
