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-

Question

Filo · Accepted Answer

Number of possible arrangements of vowels

= \frac{4 !}{2 ! 2 !} = \frac{4 \times 3 \times 2}{2 \times 2} = 6

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

1.4.4.3.2.1

ways

\Rightarrow

No. of ways

= 1 \Rightarrow 1 \times 4 \times 4 \times 3 \times 2 \times 1 = 96

.

Case II : In second place, there is a 2 vowel.

V ___ This can be formed in

4.1.3.3.2.1

ways

\Rightarrow

No. of ways =

4 \times 1 \times 3 \times 3 \times 2 \times 1 = 72

Case III : In third place there is a 2 vowel.

V ___ This can be formed in

4.3.1.2.2.1

ways

\Rightarrow

No of ways

= 4 \times 3 \times 1 \times 2 \times 2 \times 1 = 48

Case IV : In fourth place there is a 2 vowel

V ___ This can be formed in

4.3.2.1.1.1

ways

\Rightarrow

No. of ways

= 4 \times 3 \times 2 \times 1 \times 1 \times 1 = 24

No more possible case there will be a letter repeated

Thus, total ways

= 96 + 72 + 48 + 24 = 240

.

Now vowel can be arranged in 6 ways.

∴

no. of different wolds

= 240 \times 6 = 1440

.

The next cond. is : AEEA are together

No. of words

= 5! \times 2! \times 2!

Total no. of words when all four vowels are together

= 5! 2! 2! = 120 \times 2 \times 2 = 480

.

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

= 1440 - 480 = 960

Question Text	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-
Answer Type	Text solution:1
Upvotes	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-

Text solutionVerified

Practice questions from similar books