SOLUTION: Postal codes in Canada have six characters, with the first, third, and fifth characters being letters, and the other characters being digits. a)What is the maximum number of uni

Question 1105679: Postal codes in Canada have six characters, with the first, third, and fifth characters being letters, and the other characters being digits.
a)What is the maximum number of unique postal codes in Canada if the letters D, F, I, O, Q, and U are not used and neither W nor Z appears as a first character?
Answer: 18(10)(20)(10)(20)(10)= 7 200 000
b)How many of the postal codes described in part a) have the same letter repeated three times?
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.
Postal codes in Canada have six characters, with the first, third, and fifth characters being letters, and the other characters being digits.
a)What is the maximum number of unique postal codes in Canada if the letters D, F, I, O, Q, and U are not used and
neither W nor Z appears as a first character?
Answer: 18(10)(20)(10)(20)(10)= 7 200 000
b)How many of the postal codes described in part a) have the same letter repeated three times?
~~~~~~~~~~~~~~~~~~~~~

The solution for the question a)

a)  1-st character can be any of (27-6-2) = 19 letters  - 19 opportunities.

b)  2-nd character can be any of 10 digits              - 10 opportunities.

c)  3-rd character can be any of (27-6) = 21 letters    - 21 opportunities.

d)  4-th character can be any of 10 digits              - 10 opportunities.

e)  5-th character can be any of (27-6) = 21 letters    - 21 opportunities.

f)  6-th character can be any of 10 digits              - 10 opportunities.


Answer to question a) is  19*10*21*10*21*10 = 8379000 possible codes.

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