Combinatorics (Counting Principles) Unit Review

This type of sample space results when the trial involves picking with replacement, and order matters.

• Power
• Permutation
• Combination
• Multiset

This type of sample space results when the trial involves picking with replacement, and order does not matter.

• Power
• Permutation
• Combination
• Multiset

This type of sample space results when the trial involves picking without replacement, and order matters.

• Power
• Permutation
• Combination
• Multiset

This type of sample space results when the trial involves picking without replacement, and order does not matter.

• Power
• Permutation
• Combination
• Multiset

A box contains 10 white and 15 black marbles.

If seven marbles are picked from this box at random and without replacement, what is the probability that three are white and four are black?

• 0.3408

• 0.1988

• 0.0057

• 0.0097

How many distinguishable ways exist to arrange the letters in the word ELEMENTAL?

• 30,240

• 60,480

• 90,720

• 362,880

There are 20 randomly-selected people in a room. What is the probability at least one person in this room shares a birthday with someone else in this room? [Ignore leap years.]

• 41%

• 59%

• 5%

• 95%

There are 19 runners in a race. The top three runners will win a prize, with a different prize for 1st, 2nd and 3rd place.

How many possible outcomes exist for the awarding of these prizes? [Assume that there are no ties and that at least three runners finish the race.]

• 5,814

• 969

• 6,859

• 57

A group of 10 people can consist of any number of freshmen, sophomores, juniors or seniors. How many possible outcomes exist for the grade levels of the members of this group?

• 286
• 1,001
• 24,024
• 1,048,576

Krista has seven unique shirts and five unique pairs of pants. She wants to pack three of these shirts and two of these pairs of pants for a weekend trip.
How many options does she have when making this selection?

• 350
• 4,200
• 8,575
• 792

Tags

CCSS.HSS.CP.B.9