Find the number of arrangements taking all the letters of the word  CONTACTans.

The word "CONTACT" has 7 letters in total. However, the letter "T" is repeated twice.

The number of arrangements of n items taken all at a time is given by n!. However, when there are repeated items, we need to adjust this to account for the fact that swapping the repeated items doesn't create a new arrangement.

So, the number of arrangements of the word "CONTACT" is given by 7! / 2!.

Step 1: Calculate 7! 7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040

Step 2: Calculate 2! 2! =

The word "CONTACT" has 7 letters in total.

Step 1: Count the total number of letters in the word. In this case, the total number of letters is 7.

Step 2: Identify any repeating letters. In this case, the letter "C" and "T" are repeated twice.

Step 3: Use the formula for permutations of a multiset to calculate the number of arrangements. The formula is n! / (r1! * r2! * ... * rk!), where n is the total number of items, and r1, r2, ..., rk are the counts of each individual type of item.

In this case, the calculation would be 7! / (2! * 2!) = 2520 arrangements.

So, there are 2520 different ways to arrange the letters in the word "CONTACT".