Question

Find the number of ways in which the 9 letters in the word CROCODILE can be divided into three groups, each containing three letters, if the two Cs must be in different groups. [3]

Answer 1

To divide the 9 letters in the word CROCODILE into three groups, each containing three letters, with the two Cs in different groups, there are 420 possible ways.

Step-by-step explanation:

To find the number of ways to divide the 9 letters in the word CROCODILE into three groups, each containing three letters, with the two Cs in different groups, we can use the concept of combinations. First, let's consider the positions of the Cs.

We have 2 options for the first C and 6 options for the second C, giving us a total of 2 × 6 = 12 options for placing the Cs. With the remaining 7 letters, we need to divide them into two groups of 3 letters each.

We can think of this as choosing 3 letters from the 7 remaining letters for the first group, and then the remaining 3 letters form the second group. This can be calculated as C(7,3) = 35.

Therefore, the total number of ways to divide the letters is 12 × 35 = 420.