Combinations and Permutations Probability

In the word PRESENTATION there are 12 letters. You have to choose 7 of these for some reason. How many different words can you make?

• 604,800

• 792

• 5,040

• 120

How many 4-card hands that contain 3 hearts and 1 spade can be chosen from a 52-card deck?

• 3700

• 3709

• 3718

• 7436

What is the probability that the committee is made up of 3 women and 1 man?

• 2/91

• 1/20

• 3/16

• 36/91

How many ways can you arrange 2 letters from the word
S Q U A R E?

• 30

• 140

• 320

• 45

Student council has 24 members.  In how many different ways can a president, vice-president, treasurer, historian, and secretary be selected?  

• 5,100,480

• 0

• 42,504

• 5.17 x 10²¹

A team of 17 volleyball players needs to choose three players to refill the water cooler.  How many different ways can the players be chosen?  

• 3360

• 560

• 4080

• 680

Find the possibilities when a group of 15 people are going to run a race.  The top 5 finishers advance to the finals.

• 3 x 10¹²

• 120

• 3003

• 360,360

Your history teacher randomly chooses 2 out of 18 students to give an impromptu debate on freedom of press in the high school news paper.  What is the probability that both you and your best friend are chosen to give the debate?  

• 1/153

• 1/306

• 2/153

• 40/51

When does the order in which you are choose matter?

• Combination

• Permutation

Determine whether the following scenarios are a permutation or a combination:

Selecting a lead and an understudy for a school play.

• Combination

• Permutation