Number of different words that can be forrmed using all the letter | Filo

Class 11

Math

Algebra

Permutations and Combinations

565
150

Number of different words that can be forrmed using all the letters of the word "DEEPMALA" If two vowels are togehter and the other two are also together but separated from the first two is-

Solution: Number of possible arrangements of vowels

Now we have to make the cases of how this can be arranged.

Case I : In first place, there is a 2 vowel V __ this can be formed in ways

No. of ways .

Case II : In second place, there is a 2 vowel.
V ___ This can be formed in ways

No. of ways =

Case III : In third place there is a 2 vowel.
V ___ This can be formed in ways

No of ways

Case IV : In fourth place there is a 2 vowel
V ___ This can be formed in ways

No. of ways

No more possible case there will be a letter repeated

Thus, total ways .

Now vowel can be arranged in 6 ways.

no. of different wolds .

The next cond. is : AEEA are together

No. of words

Total no. of words when all four vowels are together .

Final no. of words when vowels (pair) are not together
565
150

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