1. Solve for the factorials below: a) 4! b) O! c) (3!)(2!) d) 10!/8! e) 9P f) 9Cg g) 9P5 h ) 9C5 2. a. nl (n-1 ) ! 2nl ( 20- 1 ) ! C . ( n + 3 ) ! [n +1 ) ! 3. Find n in the following equations: a) (2n + 2)!(n-1)! = S (2n)! (n+1)! b) n C2 =28 c) n C2 = 21 d) n 1/2 + n Ci = 2610. 11. 12. 13. 14. 15. 16. 17. 18. How many ways can you turn in a batting order for a baseball team if you only have 9 players? Suppose a lawyer must select 4 jurors from a set of six candidates? How many groups are possible? How many ways can 3 runners be selected for the Olympics from a field of S contestants? How many ways can the rst 3 places be awarded in a race involving 5 contestants (excluding ties)? How many ways can the positions of president and vice president be assigned from a group of 8 people? Find the Number of hugs possible in a family of 5 people (no repeat hugs). You have 9 families you would like to invite to a wedding. Unfortunately, you can only invite 6 families. How many different sets of invitations could you write? Suppose we have to select 5 managers from a list of 10. How many ways can this be done? Give the correct expression that gives the answer. Suppose we have to select a manager, assistant manager, and night manager from a list of 10 people. How many ways can this be done? Give the correct expression that gives the answer. Suppose we have an ofce of 5 women and 6 men and need to select a 4 person committee. How many ways can we select? In how many ways can 4 students be seated in a row of 20 chairs? In how many ways can 10 students be arranged in a row? A lottery consists of 54 numbers. To purchase a ticket, you select 6 numbers from 54 without repetition. How many selections are possible? (In lotteries, the order is generally not relevant.} Out of 30 applicants, 11 are female, 17 are college graduates, 7 are bilingual, 3 are female graduates, 2 are bilingual women, 6 are bilingual graduates and 2 are bilingual female graduates. Find the number of female graduates that are not bilingual. Below is a frequency table which shows the number of bathrooms in people's houses. a) Find the mode and the median of the data. b) Explain why it is not possible to nd the mean of the data presented