Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I have to find the total number of permutations of four letters that can be selected form the

word "ARRANGEMENT".

Clearly we have 7 different letters so the amount of 4 letter permutations with no repeats is:

7!/3!=840

now for each two letter can form a four letter permutaion with another two different letters

4!/(2!*2!)*6*5

where the first part gives the number of permutations of a four letter word with 2 letters the same. Each of the remaining slots can take one of the other 6 letters and the other by one of the remaining 5 letters.

Now given that there are 4 of these 180*4=720

Finally must look at all the combinations of the double letters to form a four letter permutation:

4!/(2!*2!)*3*4=72

The first part is te number of permutations of a given two letters within a four letter sequence. This is then multiplied by the number of reminaing double letters it may forma permutation with 3. This total is then multiplied by 4 the total number of double letters as any oneof them could form the inital set of permutations.

so I get a total of 72+720+840=1632.

However correct answer is 1596 can someone please explain?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Permutations problem

**Physics Forums | Science Articles, Homework Help, Discussion**