Counting Practice

The school student council consists of 8 juniors, 10 sophomores, and 12 seniors. They are forming a committee to help plan Prom. 

How many possible 4-person committees are there overall?

• 26,788

• 27,405

• 28,911

• 29,123

The school student council consists of 8 sophomores, 10 juniors, and 12 seniors. They are forming a committee to help plan Prom. 

How many possible 4-person committees could be formed that include 2 juniors and 2 seniors?

• 2,601

• 2,713

• 2,811

• 2,970

The school student council consists of 8 sophomores, 10 juniors, and 12 seniors. They are forming a committee to help plan Prom. 

How many possible 3-person committees could be formed that include 1 person from each grade?

• 745

• 860

• 960

• 1,123

The school student council consists of 8 sophomores, 10 juniors, and 12 seniors. They are forming a committee to help plan Prom. 

How many possible 4-person committees could be formed that include only seniors?

• 495

• 515

• 630

• 755

The school student council consists of 8 sophomores, 10 juniors, and 12 seniors. They are forming a committee to help plan Prom. 

How many possible 4-person committees could be formed that include no sophomores?

• 4,120

• 5,355

• 6,790

• 7,315

The school student council consists of 8 sophomores, 10 juniors, and 12 seniors. They are forming a committee to help plan Prom. 

How many ways could you select a President and a Vice President for the committee if only seniors can be chosen?

• 132

• 252

• 390

• 412

100 people are entered into a raffle. How many ways are there to choose 4 winners?

• 3,921,225

• 4,182,146

• 5,026,775

• 6,109,527

100 people are entered into a raffle. How many ways are there to choose 4 winners if the first one picked gets $20, the second picked gets $50, the third gets $100, and the last gets $5000?

• 80,672,800

• 94,109,400

• 100,674,912

• 105,629,515

There are 5 appetizers, 7 entrees, and 3 desserts on a menu.

How many ways could you select a meal that includes 1 appetizer, 2 entrees, and 1 dessert?

• 295

• 315

• 440

• 520

There are 5 appetizers, 7 entrees, and 3 desserts on a menu.

How many ways could you select a meal that includes 2 appetizers and 1 entree?

• 50

• 60

• 70

• 80