Question

The rules for license plates in Idaho are 3 letters followed by 4 numbers (example ABC 1234), where the first letter can only be the letters I, D, A, H, or O. How many different license plates can there be? In what way can Idaho increase the number of license plates?

a. 26 x 26 x 26 x 10 x 10 x 10 x 10 – Use vowels and numbers.

b. 26 x 25 x 24 x 10 x 9 x 8 x 7- keep I, D, A, H, O as the first letter

c. 24 x 25 x 26 x 7 x 8 x 9 x 10 – use 3 letters and 3 numbers

d. 5 x 26 x 26 x 10 x 10 x 10 x 10 – Allow for more first letters to be used.

Answer 1

The correct answer is option d.

Explanation:

The rules for license plates in Idaho are 3 letters followed by 4 numbers (example ABC 1234), where the first letter can only be the letters I, D, A, H, or O.

(I/ D/ A/ H/ O) ,a, a , n ,n, n, n

a = Any alphabet from 'a' to 'z'.

n = any number for 0 to 9.

Total numbers alphabets that can be used at first place = 5

Total number of alphabets = 26

Total number of numeral i.e 0 to 9 = 10

Since repetitions of alphabets and numbers are allowed.Then number of different number plates possible with this format:

`5* 26* 26* 10* 10* 10* 10=33,800,000`

Idaho increase the number of license plates by using any of alphabets from the 26 alphabets.

`26* 26* 26* 10* 10* 10* 10=175,760,000`

Answer 2

Option: d is the correct answer.

d. 5 x 26 x 26 x 10 x 10 x 10 x 10 – Allow for more first letters to be used.

Explanation:

It is given that:

The rules for license plates in Idaho are 3 letters followed by 4 numbers (example ABC 1234), where the first letter can only be the letters I, D, A, H, or O.

The number of different ways it could be done is:

as for the first place we have just 5 choices. ( as just 5 letters I, D, A, H, or O are to be used )

for the second place we have 26 choices. ( All the 26 alphabets could be used )

and same is for the third place we have 26 choices.

Now for the fourth,fifth,sixth and seventh places we have 10 choices.

Hence, the number of ways it could be done is:

5×26×26×10×10×10.

Also the number of ways the number of license plates can be increased is by not taking any restriction for the first place.

i.e. Allow for more first letters to be used.

Hence, the answer is:

Option: d

d. 5 x 26 x 26 x 10 x 10 x 10 x 10 – Allow for more first letters to be used.