ind the number of arrangements taking all the letters of the word  CONTACT

The word CONTACT has 7 letters in total. However, the letter 'C' and 'T' are repeated twice.

The formula for permutations of a multiset (where some items are repeated) is:

n! / (r1! * r2! * ... * rk!)

where:

• n is the total number of items,
• r1, r2, ..., rk are the numbers of each type of item.

In this case, n = 7 (the total number of letters), r1 = 2 (the number of 'C's), and r2 = 2 (the number of 'T's).

So, the number of arrangements is:

7! / (2! * 2!) = 5,040 / (2 * 2) = 1,260

So, there are 1,260 different arrangements of the letters in the word CONTACT.