Answer:
(a) The number of 5-letter word that can be formed (without repetition) such that the first letter is K or X is 607,200.
(b) The number of 5-letter word that can be formed (with repetition) such that the first letter is K or X is 913,952.
(c) The number of 5-letter word that can be formed (without repetition) such that the first letter is K or X and the last is J is 24,288.
Explanation:
In this case we need to form a 5 letter word.
(a)
The condition applied is: 1st letter is K or X.
The word will of the form: K _ _ _ _ or X _ _ _ _
There are 2 ways to fill the first space, i.e. with either K or X.
Repetition is not allowed.
The remaining 4 spaces can be filled in (25 × 24 × 23 × 22) ways.
Then the total number of 5-letter word that can be formed (without repetition) such that the first letter is K or X is:
Number of 5-letter word = 2 × 25 × 24 × 23 × 22 = 607200
Thus, the number of 5-letter word that can be formed (without repetition) such that the first letter is K or X is 607,200.
(b)
In case the repetition are allowed the number of 5-letter word that can be formed (without repetition) such that the first letter is K or X is:
Number of 5-letter word = 2 × 26 × 26 × 26 × 26 = 913952
Thus, the number of 5-letter word that can be formed (with repetition) such that the first letter is K or X is 913,952.
(c)
The condition applied is: 1st letter is K or X and the last letter is J.
The word will of the form: K _ _ _ J or X _ _ _ J
There are 2 ways to fill the first space, i.e. with either K or X, and the last with J.
Repetition is not allowed.
The remaining 3 spaces can be filled in (24 × 23 × 22) ways.
Then the total number of 5-letter word that can be formed (without repetition) such that the first letter is K or X and the last is J is:
Number of 5-letter word = 2 × 24 × 23 × 22 = 24288
Thus, the number of 5-letter word that can be formed (without repetition) such that the first letter is K or X and the last is J is 24,288.
