In an exacta wager you are required to pick the top two fini

In an \"exacta\" wager, you are required to pick the top two finishers in a race in the exact order in which they finished. How many exacta wagers are possible in a 8-horse race? A. 16 B. 28 C. 56 D. 112 E. 224 23. A group of 8 juniors and 4 seniors would like to form a committee for \"reasons.\" If the committee is to have four members, determine the number of ways the committee can be formed in the following situations: A. The committee chair is a senior, the committee sub-chair is a junior, and the other two members can be any combination of juniors and seniors. B. Majority of seniors

Solution

12.

8 options for first place and 7 for second place so 8*7=56 options

23.

A.

Chair is chosen in :4 ways

sub chair is chosen in :8 ways

Number of students left to choose from for other two positions: 8-1+4-1=10

So other two memeber are chosen in:C(10,2)=45

So total number of committees are: 4*8*45=1440

B.

4 people in the committee

So a senior majority is in two cases

Case 1. 3 are seniors and 1 junior

THis is done in

C(4,3)C(8,1)=4*8=32

Case 2: 4 seniors

This is done in 1 ways

So total : 33 ways