Unit 3 Lesson 4 Assignment

For each question, include the calculations that lead to your answer.

**1)** How many four-letter codes can be formed with the letters P, D, Q, X without repetition?

**2)** In how many ways can 6 bicycles be parked in a row?

**3)** In how many ways can the positions of president, VP, secretary and treasurer of the senior class be determined if there are 10 people running for office?

**4)** Sam has 5 different baseball caps. He plans to give 3 of them to different friends. In how many ways can this be done?

**5)** In how many ways can 5 people be arranged around a round table.

**6)** How many different ways can the letters of the word “PROBABILITIES” be arranged?

**7) **Find the value of each variable:

12 P 8 = [x]

8 P 8 = [y]

3 P 2 = [z]

**8**) A statistic’s teacher has received a list of 13 students to be considered for a mathematics scholarship. He is asked to rank the 4 most outstanding students. In how many different ways can he do this?

**9) **In a certain card game, a player is dealt 5 cards from a deck of 52 cards. How many different hands are possible if order matters?

**10)** In how many different ways can the letters of the word RESEARCH be arranged?