Question

Find the arrangements that can be made out of the letters of the words:
1)COMMERCE 2)STATISTICS

Answer 1

what would it be if the letters were all distinct?

Answer 2

I have no idea,I am new to this subject.

Answer 3

oh ok
counting principle

Answer 4

suppose you had 8 distinct letters
and you arrange them
8 choices for the first letter
7 for the second
6 for the third
5 for the 4th
4 for the 5th
3 for the 6th
2 for the 7th and finally
1 for the 8th
by counting principle it is the product
better known as \(8!\)

Answer 5

8 letters two repeating so,(8.7.6.5.4.3.2.1)/2.1 then? @Mimi_x3

Answer 6

not quite
in commerce you have two C, two E, and two M

Answer 7

Oh yeah..

Answer 8

so \(8!\) over counts by a factor of \(8\)

Answer 9

if you just wanted a formula it would be
\[\frac{8!}{2!2!2!}\]

Answer 10

but that is kind of silly since \(2!\) is just 2, so the denominator is 8, which cancels with the 8 up top giving you \(7!\)

Answer 11

Oh 2! three times because 3 letters are repeating 2 times?

Answer 12

right
if for example you had
googoo it would be
\[\frac{6!}{2!4!}\]

Answer 13

you should make sure you understand why that is

Answer 14

there are THREE 2!'s
in your evaluation, you only put 2 of them...

Answer 15

No... it comes out different on google.

Answer 16

OMG WAIT DUMB ME!! I LOVE YA TERENCE!

Answer 17

:)

Answer 18

Where'd you go wrong, though?

Answer 19

ahh yeah I didn't see that too...
d'oh XD

Answer 20

Same i don't know where i am wrong,AM I EVEN WRONG?!!

@nincompoop

Answer 21

you put 2x2x2 as 6
Which is 2+2+2, not 2x2x2 :P

Answer 22

Oh wait!!

Answer 23

Okay so for COMMERCE it is
8!2!2!
So that will be (8.7.6.5.4.3.2.1.)/(2.1)(2.1)
So,40,320/8=5,040...Right?

Answer 24

Yes. Much better :3

Answer 25

Let's do *STATISTICS* now,I'll do you'll see? :3 Tell me where i do wrong.

Answer 26

Me sleepy :3

Answer 27

Sleep I'm doing...then you check later? :)

Answer 28

yeah, sure... :)
---------------------------
Terence out

Answer 29

STATISTICS is 10!/3!3!2!