Question

Find all the words that can be formed by using all letters of the word 'LEARN' ? In how many of these words vowels are together ?

Answer 1

The total number of words can be formed using all letters of the word "LEARN" $:5\times 4\times 3\times 2\times 1=5!=120$
( there are a total of 5 letters in the word "LEARN". So, the first place of the word can be filled with 5 letters, second place with remaining 4 letters, third place with remaining 3 letters, fourth place with remaining 2 letters and fifth place with one letter.)
No. of vowels in word: $2$
So, both vowels can be arranged in $2$ ways together.
total number of words (vowel together): $2!\times 4!=2\times 24=48$
( when a vowel is together, there will be 4 places to fill in the word.)