Problem: The total number of ways in which the letters of the word ACCOST can be arranged such that the two Cs never come together.

Solution:
To solve this problem, we need to find the number of arrangements of the letters in the word ACCOST where the two Cs are not together. We can use the concept of permutations to solve this problem.

Step 1: Total Number of Arrangements
The word ACCOST has a total of 6 letters. The number of arrangements of these 6 letters is given by the formula n!, where n is the number of letters. So, the total number of arrangements is 6!.

Step 2: Consider the Two Cs as a Single Element
To ensure that the two Cs are not together, we can treat them as a single element. This means that we have 5 elements in total, which are A, C (treated as a single element), O, S, and T.

Step 3: Find the Number of Arrangements with the Cs Together
If we consider the two Cs as a single element, then we have a total of 5 elements to arrange. The number of arrangements of these 5 elements is given by 5!.

Step 4: Subtract the Number of Arrangements with the Cs Together from the Total Number of Arrangements
To find the number of arrangements where the two Cs are not together, we need to subtract the number of arrangements with the Cs together from the total number of arrangements.

So, the number of arrangements where the two Cs are not together is given by:
Number of arrangements = Total number of arrangements - Number of arrangements with Cs together
= 6! - 5!

Step 5: Calculate the Number of Arrangements
Using the formula for factorial, we can calculate the number of arrangements as follows:
Number of arrangements = 6! - 5!
= 720 - 120
= 600

Therefore, the total number of ways in which the letters of the word ACCOST can be arranged such that the two Cs never come together is 600.

Hence, the correct answer is option 'B'.

The word ACCOST consists of 6 letters, out of which two are the same (C). We have to see that the two Cs are never together. This can be done by considering all the possible arrangements of the letters of the word ACCOST and subtracting from it the number of ways in which the two Cs come together. The total number of arrangements of the letters of the word ACCOST considering 6 letters taken all at a time in which two letters are of one kind is 6! / 2! and the number of arrangements considering that the two Cs are together is the arrangement of 5 letters taken all at a time, i.e. ⁵P₅.