Answer:
a) 1,518,000
b) 2,284,880
c) 60,720
Step-by-step explanation:
a) a. if the first letter must be Upper C comma Upper X comma Upper T comma or Upper M and no letter may be repeated?
We draw 5 boxes, and based on that we will see the total possible cases. There are 26 alphabets
The first box should have C or X or T or M .No letter may be repeated.
Any Any Any Any Any
5 alphabets of the of the of the of the
C,X , T , M remaining remaining remaining remaining
25 alphabets 24 alphabets 23 alphabets 22 alphabets
Therefore; total possible call letters = 5 × 25 × 24 × 23 × 22 = 1,518,000
b)
The first box should have C or X or T or M Repeats as allowed
Any Any Any Any Any
5 alphabets of the of the of the of the
C,X , T , M remaining remaining remaining remaining
26 alphabets 26 alphabets 26 alphabets 26 alphabets
Therefore Total possible call letters = 5 × 26 × 26 × 26 × 26 = 2,284,880
c) The first box should have C,X , T , M and end with S
So the last place if fixed, and we now have 25 alphabets. The first box can go in 5 ways. The next box then will have only 24 letters to choose from, as the first box has taken a letter and the last box already has S in it. Repetition not allowed
Any Any Any Any S
5 alphabets of the of the of the is fixed
C,X , T , M remaining remaining remaining here
24 alphabets 23 alphabets 22 alphabets
Therefore Total possible call letters = 5 × 24 × 23 × 22 × 1 = 60,720
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