Find the number of arrangements taking all the letters of the word CONTACTans.1220126014001136
Question
Find the number of arrangements taking all the letters of the word CONTACTans.1220126014001136
Solution
The word "CONTACT" has 7 letters in total.
Step 1: Count the number of each unique letter in the word.
- C: 2
- O: 1
- N: 1
- T: 2
- A: 1
Step 2: Use the formula for permutations of a multiset: n! / (r1! * r2! * ... * rk!)
- n is the total number of items,
- r1, r2, ..., rk are the counts of each unique item.
Step 3: Substitute the counts into the formula.
- n = 7 (total number of letters)
- r1 = 2 (count of letter C)
- r2 = 1 (count of letter O)
- r3 = 1 (count of letter N)
- r4 = 2 (count of letter T)
- r5 = 1 (count of letter A)
So, the number of arrangements is 7! / (2! * 1! * 1! * 2! * 1!) = 2520.
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