Question

How many different arrangements of the letters in the word PARALLEL are there?

Answer 1

if all the letters were different it would be \(8!\)

Answer 2

56
3,360
40,320

Answer 3

but since you have 2 "A" that you cannot tell apart, and also three identical "L" it is
\[\frac{8!}{2!3!}\]

Answer 4

do you know how to compute this number?

Answer 5

Im confused

Answer 6

ok lets go slow
do you know what \(8!\) means ?

Answer 7

ya 8*7*6*5*4*3*2*1

Answer 8

if you have 8 different letters, or symbols or whatever, the number of ways they can be arranges is \(8!\) so you got that part yes?

Answer 9

ok good, but in this case you have some letters that you cannot tell apart

Answer 10

Okay im not sure how to do this srry

Answer 11

there are two "E" and the number of ways to order the 2 "E" is 2

Answer 12

and also there are 3 "L" and the number of ways to order the 3 "L" are \(3!=3\times 2=6\)

Answer 13

okay

Answer 14

so to answer your question, you have to divide
\[\frac{8!}{2!3!}=\frac{8\times 7\times 6\times 5\times 4\times 3\times 2}{2\times 3\times 2}\]

Answer 15

cancel first, multiply last

Answer 16

you can compute
\[8\times 7\times 6\times 5\times 2\] for example

Answer 17

Okay so it will be 6720

Answer 18

still probably need a calculator
i get \(3360\)
http://www.wolframalpha.com/input/?i=8*7*6*5*2

Answer 19

or just type it in directly and don't bother with the cancellation
still 3360
http://www.wolframalpha.com/input/?i=8!%2F%282!3!%29

Answer 20

O okay