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How many three-letter arrangements can be made from the letters in MOUSEPAD if no letter can be used more than once and each arrangement is made up of a vowel between two consonants?

 Jun 13, 2022
 #1
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Vowels   A , E , O , U

 

Consonants   D M  P  S

 

Choose  any 1 of the 4 vowels  = C(4,1) =  4

 

Choose any 2 of the 4 consonants  and  permute them in 2 ways =   P (4,2)  =  12

 

Total arrangements =   4 * 12   =    48

 

 

cool cool cool

 Jun 13, 2022
 #2
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Thank you so much! 

Guest Jun 13, 2022

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