Question

How many arrangements are there of the letters in the word ANAGRAM?

Answer 1

It would be \(\frac{7!}{3!}\)

Answer 2

Like take notice that there are 3 A's

Answer 3

yeah the formula you wrtoe is correct

Answer 4

Im tryna explain this concept to someone and im wondering if perhaps anyone can enlighten how to explain this concept in an easy fashion

Answer 5

i guess is 7 6 5 4

Answer 6

\[\large\rm S=\{~3A,1N,1G,1R,1M\}\]It's the number of 7-permutations of the multiset S\[\large\rm =\frac{|S|!}{3!1!1!1!1!}\]

But in an easy fashion? :ddd hmm....

Answer 7

hmmm

Answer 8

im tryna explain this concept in a concrete manner

Answer 9

instead of the student memorizing a formula I would prefer if she would be able to visualize it

Answer 10

Choose a location to place the non-repeating letters:
N (7 options)
G (6 options)
R (5 options)
M (4 options)

Fill in the remaining slots with the A's.

Answer = 7x6x5x4

That's a little more straight forward, ya? :)

Answer 11

ohhh thats a good way of looking at this

Answer 12

Thanks!

Answer 13

I'm trying to remember how to apply that logic to multiple repeated letters.
Consider 6-permutations of the word BANANA.

Using our formula we know the result should be \(\rm \dfrac{6!}{3!2!}\)

Trying to formulate it in that simpler way though...
Hmm...

Answer 14

Whatever .... I kinda think I can visualize it
I need to work on smaller samples that usually helps me

Answer 15

heh :D

Answer 16

Thanks though :)