Question

Find the number of permutations in the word “embarrass”

Answer 1

Do you know what a permutation is?

Answer 2

\[\frac{ n! }{ (n-r)! }\]

Answer 3

60,480

45,360

20,160

10,080
these are my choices

Answer 4

find out how many letters repeat and how many times they do.

Answer 5

Permutations for the word
aabbcc

= 6!/2!2!2!

Okay?

Answer 6

start off with the total number of letters,
how many are there?

then list all repeated letters and the number of times each appears.

ex.

mississippi

there are 11 letters total
i is repeated 4 times
s is repeated 4 times
p is repeated 2 times

the answer is

\[\frac{ 11! }{ 4!\,4!\,2! }\]

Answer 7

you divide because the repeated letters are not unique, but they were counted as unique in the factorial on top.

for example: bee

\[\text{be}_{1}\text{e}_{2} \text{ is the same word as }\text{be}_{2}\text{e}_{1} \]

so we don't want to count it twice and so we divide by the number of ways we could permute those objects, which of course depends on how many of them there are.

Answer 8

so for bee, there are \[\frac{ 3! }{ 2! }=3\] unique permutations of the word bee.

in fact, they are:

bee
ebe
eeb