Problem 8E

In a certain state, license plates consist of three letters followed by three numbers.

a. How many different license plates can be made?

b. How many different license plates can be made in which no letter or number appears more than once?

c. A license plate is chosen at random. What is the probability that no letter or number appears more than once?

Solution 8E

Step1 of 3:

We have license plates consist of 3 letters followed by 3 numbers.

We need to find,

a).We need to find How many different license plates can be made?

b).We need to find How many different license plates can be made in which no letter or number appears more than once?

c).We need to find A license plate is chosen at random. What is the probability that no letter or number appears more than once?

Step2 of 3:

a).

We know that the total number of letters in English = 26

The allowed digits are {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

That is n = 10.

license plates consist of 3 letters followed by 3 numbers.

Now,

The possible number of ways to made different license plates =

= 175761000

= 17576000.

Therefore, there are 17576000 ways are possible to made different license plates.

b).

We know that the total number of letters in English = 26

The allowed digits are {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

That is n = 10.

license plates consist of 3 letters followed by 3 numbers.

Now,

The possible number of ways to made in which no letter or number appears more than once is given by

= (15600)(720)

= 11232000

Therefore, there are 11232000 ways are possible to made in which no letter or number appears more than once.

Step3 of 3:

c).

If a license plate is chosen at random, the probability that no letter or number appears more than once is given by

P(the probability that no letter or number appears more than once)

=

=

= 0.6390

Therefore,The probability that no letter or number appears more than once is 0.6390.

Conclusion:

Therefore

a).There are 17576000 ways are possible to made different license plates.

b).There are 11232000 ways are possible to made in which no letter or number appears more than once.

c).The probability that no letter or number appears more than once is 0.6390.