Permutations, Combinations & Conditional Probabilities

There are ten questions on Jack’s science quiz: six multiple choice questions with four choices each and four true/false questions. How many ways can he answer the questions?

The Sandwich Shop offers combo meals with a choice of one sandwich, one side, and one drink. In total, there are 560 combos available. If there are 16 sandwiches and 5 drinks available, how many sides are there?

Marlena must answer three out of eight essay questions on her writing test. How many ways can she choose 3? Hint: Is this a permutation or combination?

The Grandview High School Band plans to play six pieces of music in their upcoming concert . How many ways can they arrange the order of their performance? Hint: Is this a permutation or combination?

How many ways can a president, vice president, and treasurer be elected from a group of 40 students?

 Josh must submit 4 paintings as part of his application to art school. If he has 25 to choose from, how many ways can he pick 4?

How many different 12-letter arrangements can be made using the letters in the word CARELESSNESS?

The field hockey coach chooses players to put away equipment after each practice. If there are 16 players on the team, how many ways can she choose five?

Kate is randomly choosing a date in the month of August. What is the probability that she chooses a two-digit number or a prime number? Write your answer as a fraction.

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CCSS.HSS.CP.B.7

Erik is randomly choosing a card from a standard deck. What is the probability that he chooses a card that is red and a multiple of three? Write your answer as a fraction.