Math help! 10 points first answer =)?

Question

how many different orderings can you make out of the letters A, B, C & what are they?

ex. ABC ACB BAC etc

how many orderings (like one above) can you make out of the letters ABCD & what are they?

how many orderings can you make out of ABCDE? i dont need to know what they are there is A TON. haha thanks.

Answer 1

i cant tell you what are they but there is a trick to find how many combos if there are 3 letters only EX:ABC you do 3 times 2 times 1

if there is 4 letters 4 times 3 times 2 times 1

and i believe the combos for ABC are ABC ACB BAC BCA CAB and CBA

Answer 2

abc, acb, bac, bca, cab, cba - 6

abcd, abdc, acbd, acdb, adbc, adcb,

bacd, badc, bcad, bcda, bdac, bdca

cabd, cadb, cbad, cbda, cdab, cdba,

dabc, dacb, dbac, dbca, dcab, dcba - 24

120  for last one

Answer 3

I could have told you to do your own homework, but I'll be kind and do it for you since I've got nothing else to do...

Since you can't repeat a letter twice, you do

3*2*1 = 6, there is 6 different orderings, now we need to find them

1. ABC

2. ACB

3. BAC

4. BCA

5. CBA

6. CAB

With the D we do 4*3*2*1 = 24, there is going to be 24 here are they:

1.ABCD

2.ABDC

3.ACBD

4.ACDB

5.ADBC

6.ADCB

7.BACD

8.BADC

9.BCAD

10.BCDA

11.BDAC

12.BDCA

13.CABD

14.CADB

15.CBAD

16.CBDA

17.CDAB

18.CDBA

19.DABC

20.DACB

21.DBAC

22.DBCA

23.DCAB

24.DCBA

Hope I helped!

Answer 4

ABCDE

BCDEA

CDEAB

DEABC

EABCD

OK I AM TIRED....

Answer 5

do ur own homework

Answer 6

if the letters cannot be repeated, ABC can be arranged in 6 different ways:

ABC

BCA

CBA

BAC

ACB

CAB

Mainly, the formula can be explained by:

First letter - you have 3 choices

Second letter - you only have two choices because the first has been taken by the first letter

Third letter - only one is left

so:

3(2)(1) = 6 combinations

Using the same formula for ABCD

4(3)(2)(1) = 24

and for ABCDE

5(4)(3)(2)(1) = 120 combinations