Math Is Fun Forum

shocamefromebay

Member

Registered: 2007-05-30

Posts: 103

Probability

Ok, I have a question that I just cannot figure out.

I want to find out how many five letter strings I can make if none of the letters are the same. The string must also be in alphabetical order.

For example, ABCDE is okay, but ABCED is not.

Can any one help me?

The only real killer part that I can't figure out is the alphabetical order part.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Probability

Hi shocamefromebay;

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Probability

hi shocamefromebay

Suppose you have found all the ways of using A, B, C, D, and E in some order.

There are 5! = 5x4x3x2x1 = 120 of these.

But only one will be in the correct ( alphabetical ) order so dis-allow 119 possibillities.

But this will be true for any five letters.

eg B, Z, Y, T, and P can only be allowed if the order is BPTYZ, again that is 119 ways, with these letters, dis-allowed.

So to get your answer, take the number of ways (without order considerations) and divide by 120; that should give you the result you want.

Bob

Last edited by Bob (2011-01-17 23:56:53)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

FERMAT'S

Member

Registered: 2011-01-17

Posts: 29

Re: Probability

I got the same bobbym's answer

65780 ways = 26C5

thank u for the quastion

Last edited by FERMAT'S (2011-01-18 18:32:34)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Probability

That is very good FERMAT's and Bob Bundy!

Yes, that was the hint. For every 5 letters there are 120 ways to arrange them but only one is in alphabetical order.

Everybody helped but so far he has not come back.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.