Combinatorics - 3 odd

A license plate format in a certain state consists of five letters followed by two digits. If once a letter or digit is used, it cannot be used again, how many different license plates could this state potentially issue in this format?

• 710,424,000
• 2,960,100
• 1,188,137,600
• 8,347,680

Tags

CCSS.HSS.CP.B.9

From 25 members of the music club, four are chosen to be officers: President, Vice President, Secretary and Treasurer.
In how many ways can the officers be chosen?

• 303,600
• 12,650
• 390,625
• 20,475

Tags

CCSS.HSS.CP.B.9

80 students apply to go on a special field trip, but there is only space for 20 students, so the Principal is going to choose at random from among the applicants to decide who gets to go on the trip.
Cindy, Macy and Tracy are friends and they have all applied to go on this field trip. What is the probability that this entire group of friends gets to go on the field trip together?

• 0.0139
• 0.4165
• 0.0375
• 0.5935

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

• 30,240
• 60,480
• 90,720
• 362,880

At a restaurant, there are 10 beverages, 5 salad choices, 6 main courses, and 3 desserts. How many possible meals can be made?

• 90

• 180

• 300

• 900

There are 15 players on a basketball team. In how many ways can the coach select the 5 starting players?

• 120

• 360,360

• 12,454,041,600

• 1,307,674,368,000

A certain marathon had 50 people running. Prizes are awarded to the runners who finish in 1st, 2nd, and 3rd place. How many different possible outcomes are there for the first 3 runners to cross the finish line?

• 254,251,200

• 5,527,200

• 125,000

• 117,600

Determine if this question is asking for a permutation or a combination.

How many 3 person committees are possible when selected from a pool of 10 people?

• Permutation

• Combination

How many possible 3 person committees are possible when selecting from a pool of 10 people?

• 45

• 90

• 120

• 720

How many hands of 5 playing cards can be dealt using a standard deck of 52 cards?

• 311,875,200

• 133,784,560

• 5,197,920

• 2,598,960