An order of award presentations has been devised for seven people: Jeff, Karen, Lyle, Maria, Norm, Olivia, and Paul. 32) In how many ways can the men be presented first and then the women? 32) Solve the problem. 33) There are 10 horses in a race. In how many ways can the first three positions of the order of the finish occur? (Assume there are no ties.) 33) 34) In how many ways can the letters in the word PAYMENT be arranged if the letters are taken 5 at a time? 34)

A class has 32 students. In how many different ways can four students form a group for an activity? (Assume the order of the students is not important.) C.. There are different ways that the four students can form a group for an activity. (Type a whole number.)

15) Use the situation below to answer the question that follows. Team Jet has 7 members who won a school competition. Of these 7, 4 members are randomly picked to receive prizes for winning. The 1st member selected wins a $50 gift card; the 2nd person selected wins a $25 gift card; the 3rd person selected wins a $10 gift card; the 4th person selected wins a $5 gift card. The names of Team Jet's members are represented by the first letter of their first names, as displayed in the following table: Name Frank Gina Harriet Inez Jakob Keven Liu Letter F G H I J K L In the box below, complete the remaining three rows of the list that models how to calculate the number of possible ways 4 team members can be selected to win the prizes. 1) FGHIJKL Let Lui win the 1st prize, so select L. 2) 3) 4)