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?

• Combination

• Permutation

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?

• Combination

• Permutation

Evaluate.

• 4

• 20

• 10

• 40

Evaluate.

• 16,016

• 8,008

• 9,382

• 4,822

Evaluate.

• 1001

• 1000

• 999

• 1001000

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?

• 20

• 120

• 40

• 3360

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?

• 8,648,640

• 5040

• 1716

• 13

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?