Question

A small island country with less than 20,000 cars has decided to reissue the license plates for its cars and has decided on the following rules for assigning numbers and letters to the license plates. Each plate will have 7 character positions that each must be filled. The leftmost character position will hold a letter from the set {D, E, H, G, X}. The next three positions will hold integers from the set {0, 1, ..., 9} but none of the integers can be repeated. The rightmost three positions must be entirely from the set {I, V, X} or entirely from the set {P, Q, R}, with repetition allowed in either case. For example, a valid plate would be G 027 XXI and an invalid plate would be G 337 PQX (two rules violated). What is the maximum number of different license plates following the rules?

a. 270,000
b. 2,624,400
c. 3,645,000
d. 194,400

Answer 1

The maximum number of different license plates following the rules is 2,624,400.

Step-by-step explanation:

To determine the maximum number of different license plates following the given rules, we need to multiply the number of choices for each character position.

For the leftmost character position, we have 5 choices (D, E, H, G, X).

For the next three integer positions, we have 10 choices for the first position, 9 choices for the second position (since one integer cannot be repeated from the previous choice), and 8 choices for the third position (since two integers cannot be repeated from the previous choices).

For the rightmost three positions, we have 3 choices each from the set {I, V, X} or {P, Q, R}, allowing for repetition within each set.

Therefore, the maximum number of different license plates is 5 * 10 * 9 * 8 * 3 * 3 * 3 = 2,624,400.

Answer 2

The answer is "Choice d"

Step-by-step explanation:

Given data:

7 position
`5, 10 , 9, 8 , 2 * 3^3`

calculating the left most filled by any of D, E, H, G, X

a possible way to fill =5

calculating the next 3 value that will be filled 0 to 10 without any repetition

possible way to fill
`=10 * 9 * 8`

calculting the last filled any if set
`\{I,V,X\} \ \ or \ \ \{P,Q,R\}` with repetation

possible way
`=2 * 3^3`

Total different licence plates
`= 5 * 10 * 9 * 8 * 2 * 3^3=194400`