How many distinct arrangements can be formed from all the letters of "students"? Please show your work. Thanks!
1 answer:
There are a total of 8 letters in student, with 6 different letters ( there are 2 s's and 2 t's).
First find the number of arrangements that can be made using 8 letters.
This is 8! which is:
8 x 7 x 6 x 5 x 4 3 x 2 x 1 = 40,320
Now there are 2 s's and 2 t's find the number of arrangements of those:
S = 2! = 2 x 1 = 2
T = 2! = 2 x 1 = 2
Now divide the total combinations by the product of the s and t's:
40,320 / (2*2)
= 40320 / 4
= 10,080
The answer is A. 10,080
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