My Math Forum How many words of seven letters

 September 23rd, 2011, 06:20 AM #1 Newbie   Joined: Sep 2011 Posts: 29 Thanks: 0 How many words of seven letters There are letters {a, a, a, b, e, e, c } How many words of seven letters - different letter queues - can be formed of them? There has to be for example two times a and so on in the word. My solution is just n over k: 7 4 ( 7, because there are 7 characters and 4 because there are 4 different characters, three are similar )
September 23rd, 2011, 08:37 AM   #2
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Re: How many words of seven letters

Hello, mike688!

Quote:
 There are letters {a, a, a, b, e, e, c } How many differentwords of seven letters can be formed of them? My solution is just n over k:[color=beige] .[/color]$7\choose4$ [color=beige] .[/color] [color=blue] . . . No[/color]

If we had seven different letters, there would be $7!$ possible permutations.

Since the three $a$'s are identical, our number is too large by a factor of $3!$

Since the two $e$'s are identical, our number is too large by a factor of $2!$

[color=beige]. . [/color]The number of permutations is:[color=beige] .[/color]$\frac{7!}{3!\,2!} \:=\:420$

 September 23rd, 2011, 09:56 AM #3 Newbie   Joined: Sep 2011 Posts: 29 Thanks: 0 Re: How many words of seven letters Soroban, thank you very much!

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