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What is the the number of words that can be formed by the first 8 letters of the...

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babyryan95 | Honors

Posted July 6, 2012 at 3:02 AM via web

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What is the the number of words that can be formed by the first 8 letters of the alphabet using 5 letters at a time.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted July 6, 2012 at 3:47 AM (Answer #1)

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While forming words given a set of letters, the order in which the letters are placed is important. For example net, ten and ent are three different words.

When words are being formed using the first eight letters of the alphabet taking 5 at a time, there are 8 different letters that can be placed at the first position, 7 different letters than can be placed at the 2nd position,..., 4 different letters than can be placed at the 5 place.

This gives the total number of words as: 8*7*6*5*4 = 6720

The number of words that can be formed using the first 8 letters of the alphabet using 5 letters at a time is 6720

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chaobas | College Teacher | Valedictorian

Posted July 6, 2012 at 4:08 AM (Answer #2)

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The number of combination of 5 letter formed by using first 8 letter of alphabet can be found out by using permutation formaula.

 

nPr = n!/(n-r)!

were n is the number of letter and r is number of letter taken at a time that is n = 8 and r = 5

 

so 8P5 = 8!/(8-5)! = 8!/3!  [n! = 1*2*3*4*5*.......*n]

= (1*2*3*4*5*6*7*8)/(1*2*3)

=6720

 

so the number of 5 letter word that can be formed from first 8 letter of alphabet is 6720 words

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