Question

how many words can be made by using all letters of the word "Mathematics" in which all vowels are """'never""" together ?? (from class 11 mathematics Ch permutations and combinations )please read the question properly​

Answer 1

Step-by-step explanation:

First find all the possible permutations of the word mathematics

Which is, 11! / (2! × 2! × 2!). Since the letters M A T are repeated two times.

Then find the number of cases in which all vowels are together.

Which is, There are four vowels. Consider them as a single block.

Total number of permutations will be (8! × 4!) / (2! × 2! ×2! ). The 4! is here because the block of four vowels can again arrange themselves in 4! ways.

Now subtract them to get the required answer.

Answer 2

Answer:

To find the number of words in which vowels are never together, we have to subtract the number of words in which the vowels come together from the total number of words which can be formed .

total number letters present is 11 .

M is repeated twice,T is repeated twice and A is repeated twice.

therefore total number of permutations will be 11 !/2!×2!×2!

Then to find the number of words in which vowels do not come together, we consider all the vowels as a single unit and find the number of permutations in which they come together.

therefore the number of permutations will be

8!/2!×2! × 4!/2!

(multiplying by 4!/2! for the number of permutations of vowels. here A repeat twice.)

The to find the number of words in which vowels do not come together subtract the above two.

I have tried to give a detailed explanation. Hope you understand