Solve the following problems. Show all your work! You May Use Excel ... I would!

1. How many three letter security codes are possible with replacement. Assume all the alphabet is in the sample space.

2 .You have been asked to create license plates for the City of Asheville, NC. Suppose license plates are to have three letters followed by three digits, and the first digit cannot be zero

a. How many different license plates can be made (replacement is okay)?

b. How many different license plates can be made if letters cannot be duplicated?

3. How many committees of 5 people can be formed from a group of 15 people (order does not matter)?