the total nnumber of words that can be made by writing the letters of the word PARAMETER SO THAT NO VOWEL IS BETWEEN 2 CONSONANTS

Dear Shivam ,

the given word is PARAMETER.

and between every 2 consonants there is a vowel.

so given condition is that THERE IS NO VOWEL BETWEEN 2 CONSONANTS

so for that , we have to take all the vowels to ONE SIDE and FOR NOW treat them as a SINGLE letter.

vowels are : A , A , E , E

Consonants : P , R , M , T , R

let us take AAEE as one.

so total number = 5 + 1 = 6 (5 consonants + 1 vowel)

and number of words that can be made = 6! = 720

but the vowels can also be arranged in 4! / 2!*2! ways because 'A' appears twice and 'E' appears twice. =  6

so total number of words = 720 * 6 = 4320.

 

Please approve !

Dear student,

Keep all vowels together and all consonants together we have following ways:

4! * 4! /2! 2! 2!

 

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Askiitians Expert

Sagar Singh

B.Tech, IIT Delhi

If we take all the vowels together that is AAEE then we can arrange them by 4!/2!*2! = 6 Now all the continents can be arranged by 5!/2!=60And now you can place the consonants in 5 days around the vowels •A•A•E•E• ...... (• denotes the ways you can arrange number of words that can be made by using all the letters of word parameter so that no one is between two consonants)So the total answer is 6*60*5 = 1,800Show the final answer is ,1800