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# How many words can we make for the PERMUTATIONS word using only one vo

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Re: How many words can we make for the PERMUTATIONS word using only one vo [#permalink]

Also please correct me for the below steps :

Total Vowels : 5 (EUAIO)
Total Consonants: 7 (Remaining letters)

3 places to be filled : — — —
2 consonants can be chosen in 7C2 ways
2 consonants can be arranged in 2! Ways
Middle place to be filled with vowel , hence, 5C1 ways

Hence total ways : 7C2 * 2! * 5C1 = 210.

Can you please highlight where am I going wrong here and what am I missing out???
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Re: How many words can we make for the PERMUTATIONS word using only one vo [#permalink]
Anamika1496 wrote:

Also please correct me for the below steps :

Total Vowels : 5 (EUAIO)
Total Consonants: 7 (Remaining letters)

3 places to be filled : — — —
2 consonants can be chosen in 7C2 ways
2 consonants can be arranged in 2! Ways
Middle place to be filled with vowel , hence, 5C1 ways

Hence total ways : 7C2 * 2! * 5C1 = 210.

Can you please highlight where am I going wrong here and what am I missing out???

Hi,

There are two T in the word and they will form the same set of words, hence you are double counting the words in 7C2.

I think you need to consider cases and solve this. I have shared my attempt of the question, let me know if you have questions.
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Re: How many words can we make for the PERMUTATIONS word using only one vo [#permalink]
I tried this way;
no of ways of selection of vowels =5
whatever will be selection procedure for consonants ,product of both will be a multiple of 5.
Hence 155.
Re: How many words can we make for the PERMUTATIONS word using only one vo [#permalink]
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