How many four letter words can be formed using the letters of the word 'FAILURE', so that (1) F is included in each word ? (2) F is not included in any word ?
The word is FAILURE.
(1) The alphabet F should be in every four letter word.
Out of the alphabets A, I, L, U, R and E, we need to choose three alphabets.
This can be done in 6C3= 20 ways.
Now, the four alphabets can be arranged in 4! ways = 24.
Required number of ways = 20 x 24 = 480.
(2) The alphabet F is not included.
Total number of four letter words that can be formed =4! x 7C3 = 840 ways
Total words in which F is not there = 840 - Total words in which F is there = 840 - 480 = 360