In a certain country license plates consist of zero or one digit followed by four or five uppercase letters from the Roman alphabet. (a) How many different license plates can the country produce?
(b) How many license plates have no repeated letter? (c) How many license plates have at least one repeated letter?
(d) What is the probability that a license plate has a repeated letter? (Round your answer to the nearest whole percent.)

Step-by-step explanation:

From the given information:

The number of different license plate the country  can produce is in the form:

=L₁L₂L₃L₄   or  L₁L₂L₃L₄L₅  or  D₁L₁L₂L₃L₄   or    D₁L₁L₂L₃L₄L₅

∴

The Total number of the license plate that can be produced is;

= 26⁴ + 26⁵ + (10 × 26⁴) + (10 × 26⁵)

= 456976 + 11881376 + 4569760 + 118813760

= 135721872

Number of license plate with no repeated letter = P(26,4) + P(26,5) + 10 P(26,4) + 10 P(26,5)

= 11 P(26,4P + 11 P(26,5)

= 90776400

c) The number of the licensed plate with 1 repeated letter = Total number of the licensed plate - number of the licensed plate with no repeated letter.

= 135721872 - 90776400

= 44945472

d) The probability that a licensed plate has repeated letter is:

= 33.12%

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