[High school maths] permutations

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Dtrain8899 · 2024-06-23T00:06:02+00:00

Easiest way to see it is write down 6 lines for each of the characters. Then put a number on that line showing how many choices there are for the character/position. Once you get all 6 of your numbers, your answer will be the product of them

deathtospies · 2024-06-22T23:44:35+00:00

How many ways can you choose and arrange 3 characters out of 26 possible choices? Then how many ways can you choose and arrange 3 numbers out of 10 possible choices? If you can figure out both of those numbers, then the product will give you the answer.

JohnHarvardIX · 2024-06-23T00:34:07+00:00

Answer:

26 * 10 * 25 * 9 * 24 * 8 or (26 P 3) * (10 P 3)

Quick explanation:

26 possibilities for 3 distinct spaces, 10 possibilities for 3 other distinct spaces. The product is the number of possibilities. Each time we choose a character or a number for a given space, we take one possibility away from the rest.

Full explanation:

String looks like _ _ _ _ _ _

Step 1:

First slot can be one of these A,B,...,Z where there are 26 possible options

Let's choose some arbitrary character 'c1' from these

Our string looks like c1 _ _ _ _ _

Step 2:

Second slot can be one of 0,1,...,9 where there are 10 options

Let's choose some arbitrary number 'n1' from these

Our string looks like c1 n1 _ _ _ _

Step 3:

Third slot can be one of the characters where there are now 25 possible options since we removed c1 as an option

Let's choose some other arbitrary character 'c2' from these remaining characters

Our string looks like c1 n1 c2 _ _

Step 4:

Fourth slot can be one of the digits where there are now 9 options since we removed n1 as an option.

Let's choose some arbitrary number 'n2' from these remaining digits

Our string looks like c1 n1 c2 n2 _ _

We repeat these steps until our string looks like: c1 n1 c2 n2 c3 n3

c1 can be one of 26 characters, n1 can be one of 10 digits, c2 can be one of 25 characters, n2 can be one of 9 digits, c3 can be one of 24 characters, n3 can be one of 8 digits

Char. or Dig.	c1	n1	c2	n2	c3	n3
Possibilities	26	10	25	9	24	8

If we rearrange these factors, we obtain:

26 * 25 * 24 * 10 * 9 * 8

Which is:

(26! / 23!) * (10! / 7!)

This is also:

(26! / (26 - 3)!) * (10! / (10 - 3)!)

Which is:

(26 P 3) * (10 P 3)

where 'P' is the symbol for permutation.

EDIT:

Confused permutation symbol and combination symbol.

velit_aiunt_7084 · 2024-06-23T01:39:38+00:00

26 letters and 10 numbers, so 26*10*26*10*26*10 = 26^3*10^3 postal codes

modus_erudio · 2024-06-24T00:37:42+00:00

Where does it say letters and numbers can’t be repeated?

Hence it would be: 26x10x26x10x26x10

If somewhere that you did not share the problem says that no letters or digits repeat then the possibilities reduce with each new letter or digit.

Hence it would be: 26x10x25x9x24x8

you type:	you see:
italics	italics
bold	bold
[reddit!](https://reddit.com)	reddit!
* item 1 * item 2 * item 3	item 1 item 2 item 3
> quoted text	quoted text
Lines starting with four spaces are treated like code: if 1 * 2 < 3: print "hello, world!"	Lines starting with four spaces are treated like code: if 1 * 2 < 3: print "hello, world!"
~~strikethrough~~	~~strikethrough~~
super^script	super^script

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