Question

1)

A set of license plates has four letters followed by 4 digits.

(a)

In how many ways can a license plate be made with four letters followed by 4 digits? (Letters or digits may be repeated.)

(b)

In how many ways can a license plate be made with four different letters followed by 4 different digits?

(c)

If a license plate is made with four letters followed by 4 digits, what is the probability that it has no repeated letters or digits? (Enter your probability as a fraction.)

2)

The County Parks and Recreation Board is planning to upgrade the playground equipment in 5 of the 18 county-owned parks in the first phase of making their parks safer for the children who play there. In how many ways can they select 5 of those parks to receive the upgrades in the first phase?

3)

A medical student is given a list of 12 hospitals and must select 4 of them at which she would be interested in serving as an intern. The order of selection is not important. In how many ways can she make her selection?

Answer 1

1)

a)

Number ways a license plate made with four letters followed by 4 digits

Number of ways 4 letters selected from 26 letters with repetitions allowed = 26 x 26 x 26 x 26=456976

Number of ways 4 digits selected from 10 digits(0 to 9) with repetitions allowed = 10x10x10x10=10000

Number ways a license plate made with four letters followed by 4 digits = 456976 x 10000 = 4569760000

(b)

In how many ways can a license plate be made with four different letters followed by 4 different digits

Number of ways 4 letters selected from 26 letters with no repetitions allowed = 26 x 25 x 24 x 23=358800

Number of ways 4 digits selected from 10 digits(0 to 9) with repetitions allowed = 10x9x8x7=5040

Number of ways a license plate be made with four different letters followed by 4 different digits = 358800 x 5040=1808352000

(c)

probability that it has no repeated letters or digits

= Number of ways a license plate be made with four different letters followed by 4 different digits / Number ways a license plate made with four letters followed by 4 digits

= 1808352000 / 4569760000

2)

Number county-owned parks = 18

Number of play grounds  County Parks and Recreation Board is planning to upgrade = 5

Number of ways 5 can be selected from 18 country-owned parks =

Number of ways they can select 5 of those parks to receive the upgrades in the first phase = 8568

3)

Number of hospitals in the list that is given = 12

Number of hospitals that the medical student can select = 4

Number of ways of selecting 4 hospitals from 12 hospitals =

Number of ways she can make her selection = 495