# Alg2

posted by Rock

what is the number of possibilities of arrangements of the letters in the word intercept?

1. MathMate

When there is no repetition of the letters, the number of permutations (order counts) is nPr, taking r letters at a time n!/(n-r)!.
If all n letters are taken (as in the present case) to make the word, nPn reduces to
n!/(n-n)!=n!/0!=n!/1 = n!

However, if there are repetitions of letters, we have to reduce the number of permutations by the factor r1! for each occurrence of the duplication/repetition.

Examples:
1. How many arrangements of the six letters of the word "number" are there?
6 letters, no repetitions, 6P6=6!=720.

2. How many arrangements of the eleven letters of the word "mathematics" are there?
We note repetitions of the letters m(2), a(2), t(2), so the number of arrangements
= (11P11)/(2!2!2!)
=11!/(2!2!2!)
=4989600

## Similar Questions

1. ### Math

A license plate is to consist of two letters followed by three digits. How many different license plates are possible if the first letter must be a vowel, and repetition of letters is not permitted, but repetition of digits is permitted?
2. ### maths

The number of arrangements of five letters from the word 'magnetic' that contain the word net is: a)60 b)100 c)360 d)630 e)720 we're still doing this at school and I still don't get it; since I have to use three of the eight letters …
3. ### math

how many arrangements can be formed from all the letters in the word parallel?
4. ### math

How many different arrangements of two letters can you make from the letters in the word problem, if no repetition of letters is allowed?
5. ### Alg2

# of possibilities of arrangements for the word intercept?
6. ### Math

How many different arrangements can be made with the letters from the word ORANGE?
7. ### spanish

need help unscrambling these letters to make a phrase first word is 3 letters second word is 6 letters and the last word is 15 letters. esosaaapahilbnoehstlsipn
8. ### math

Find the number of arrangements of the letters of the word STRENGTH if the order of the consonants must not be changed?
9. ### Algebra 2

How many arrangements are possible using the letters in the word FUZZY if each letter "Z" is distinctly different than the other?
10. ### Math

Determine the number of different six letter arrangements that can be formed with the letters GUIDEPOST if the last two letters must be vowels?

More Similar Questions