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Question

The serial number on a new twenty-dollar bill consists of two letters followed by nine digits and then a letter. How many different serial numbers are possible, given the following conditions?



(a) Letters and digits cannot be repeated.

(b) Letters and digits can be repeated.

  

(c) The first and last letters are repeatable vowels, the second letter is a consonant, and the digits can be repeated. (Let y be a consonant)

Answer 1

a. By the given conditions and the Fundamental Counting Principle, we have that the total number of serial numbers possible is 26*25*10*9*8*7*6*5*4*3*2*24 = 56,609,280,000

b. By the given conditions and the Fundamental Counting Principle, we have that the total number of serial numbers possible is 26*26*10*10*10*10*10*10*10*10*10*26 = 17,576,000,000,000

c. By the given conditions and the Fundamental Counting Principle, we have that the total number of serial numbers possible is 5*21*10*10*10*10*10*10*10*10*10*5 = 525,000,000,000