My Math Forum Permutation

 January 29th, 2010, 05:45 AM #1 Newbie   Joined: Jan 2010 Posts: 2 Thanks: 0 Permutation Calculate the number of ways to arrange all the letters of the word 'LONGITUDES' if all the vowels are separated from each other. Thanks a lot for your help!
January 29th, 2010, 09:12 AM   #2
Math Team

Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 408

Re: Permutation

Hello, cyt_91!

Quote:
 Calculate the number of ways to arrange all the letters of the word 'LONGITUDES' if all the vowels are separated from each other.

There are 6 consonants and 4 vowels.

Place the 6 consonants in a row with spaces before, after and between them:

[color=beige]. . [/color]$_{-}\;C\;_{-}\;C\;_{-}\;C\;_{-}\;C\;_{-}\;C\;_{-}\;C\;_{-}$

$\text{The 6 consonants can be arranged in }6!\text{ ways.}$

$\text{Select 4 of the the 7 spaces in which to place the vowels: }\:{7\choose4}\text{ ways.}$

$\text{The 4 vowels can be arranged in }4!\text{ ways.}$

$\text{Therefore, there are: }\:(6!){7\choose4}(4!) \;=\;(720)(840)((24) \;=\;14,515,200\text{ arrangements.}$

 Tags permutation

### how to calculate permutation with vowel separated

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post abramo_k Algebra 4 February 27th, 2013 12:11 PM kingkos Algebra 1 December 6th, 2012 12:39 PM kingkos Algebra 0 December 5th, 2012 10:43 AM panky Algebra 8 November 21st, 2011 11:11 PM cyt_91 Advanced Statistics 1 January 29th, 2010 07:16 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top