Counting Principle

How many different four-letter passwords can be formed from the letters A, B, C, D, E, F, and G if no repetition of letters is allowed?

Fifty people purchase raffle tickets. Three winning tickets are selected at random. If each prize is $500, in how many different ways can the prizes be awarded?

Evaluate.

Evaluate.

Evaluate.

Evaluate.

An election ballot asks voters to select three city commissioners from a group of six candidates. In how many ways can this be done?

You have time to watch 7 movies on Netflix from your favorite list of 13 movies. In how many ways can you watch these if you start with your least favorite to your most favorite?

In how many distinct ways can the letters of the word DALLAS be arranged?

(a)  

A television programmer is arranging the order in which five movies will be seen between the hours of 6 p.m. and 4 a.m. Two of the movies have a G rating, and they are to be shown in the first two time blocks. One of the movies is rated NC-17 and it is to be shown in the last of the time blocks, from 2 a.m. until 4 a.m. Given these restrictions, in how many ways can the five movies be arranged during the the indicated time blocks?