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how many different words can be formed with the letter of the word EQUATION so that the words begin and end with consonant?

how many different words can be formed with the letter of the word EQUATION so that the words begin and end with consonant?
 

Grade:11

1 Answers

Vikas TU
14149 Points
6 years ago
In the word EQUATION there are 5 vowels(A,E,I,O,U) and 3 consonants (Q,T,N)
                                There are 8 letters in EQUATION,
                 So to form different words that begin and end with consonants,
                The first word can be filled with any of the three consonants – 3 ways
                 The last word can be filled with any of the remaining two consonants – 2 ways
                 The second word can be filled with any of the five vowels – 5 ways
                The third word can be filled with any of the remaining four vowels – 4 ways
                 The fourth word can be filled with any of the remaining three vowels – 3 ways
                The fifth word can be filled with any of the remaining two vowels – 2 ways
                The sixth word can be filled with the remaining one vowels  - 1 way
                The seventh word can be filled with the remaining one consonant – 1 way
So Total no. of words = 3*2*5*4*3*2*1*1=720 words

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