Find the number of arrangements taking all the letters of the word CONTACT
Question
Find the number of arrangements taking all the letters of the word CONTACT
Solution
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 there are repeated elements) is:
n! / (r1! * r2! * ... * rk!)
where:
- n is the total number of elements,
- r1, r2, ..., rk are the numbers of each type of repeated element.
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 word "CONTACT".
Similar Questions
Find the number of arrangements taking all the letters of the word CONTACTans.1220126014001136
Find the number of permutations of the letters of the word MISSISSIPPI.
In how many ways can the letters of the word 'ARRANGE' be arranged? How many of these arrangements are in which (1) two R's come togethe
What is the number of arrangements that can be made with the letters of the word CAREFUL so that the vowels occupy even places?Question 2Answera.144b.120c.720d.36
In how many ways can the letters of the word PERMUTATIONS be arranged if the words start with P and end with S?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.