Question

If we permit 5 letters of the word lemon in 5! Ways.In how many word vowels do not come together

Answer 1

Answer: There are 72 words in which vowels do not come together.

Step-by-step explanation:

There are two vowels in the word lemon.

To find the number of words in which vowels do not come together, we need to find the number of words in which vowels come together then subtract it from total number of words.

Using string method, tie the two vowels with a string and suppose the vowels as a one unit.

So, the number of words in which vowels come together= 2! 4!

= 2x1x4x3x2x1=48

Total number of words= 5!= 5x4x3x2x1= 120

So,  

The number of word in which vowels do not come together= 120-48= 72