An electronics store receives a shipment of 20 graphing​ calculators, 33 that are defective. Four of the calculators are selected to be sent to a local high school.   ​(A) How many selections can be​ made? ​(B) How many of these selections will contain no defective​ calculators?

A bagel shop has a selection of 8 different kinds of bagels (at least 10 of each). (.1) How many different selections of 10 bagels can be made? ( .2) If garlic is one kind of available bagel and onion is another, how many different selections of 10 bagels can you make so that you have at least 3 onion bagels and exactly 2 garlic bagels?

Scientists have found a way to distinguish chronic-fatigue syndrome (CFS) from post-treatment Lyme disease by different proteins in a patient's spinal fluid. In a study of 4334 patients, the results to the right were found. (a) How many had the protein for Lyme only? (b) How many had the normal protein only? (c) How many had none of the proteins? 1654 had the protein for normal patients, CFS, and post-treatment Lyme disease; 1754 had the protein for CFS and Lyme; 820 had the protein for CFS only; 2660 had the protein for CFS; 1759 had the normal protein as well as the one for Lyme; 2625 had the protein for Lyme; 2648 had the normal protein. (a) There were 766 patients who only had the protein for Lyme. (Type a whole number.) (b) There were patients who only had the normal protein. (Type a whole number.)

We are interested in looking at the effect of a baseball player’s free agent status on their salary. We look at 337 baseball players and categorize them as either having a high salary (above 2 million) or not, and as either being free agents or not. ------------------------------ You also wonder if having a high batting average affects the salary of baseball players. You classify all 370 baseball players as having a high batting average if it is over .300.   1. The given χ2test table gives many test statistics. The row we want to look at is labeled Pearson Chi-Square. Give the test statistic, the degrees of freedom, and the p-value. 2. At a significance level of .05, what can you conclude in the context of this problem?

There are 22 members of a basketball team. (1) The coach must select 8 players to travel to an away game. How many ways are there to select the players who will travel? (2) From the 8 players who will travel, the coach must select her starting line-up. She will select a player for each of the five positions: center, right forward, left forward, right guard, left guard. How many ways are there for her to select the starting line-up? (3) From the 8 players who will travel, the coach must select her starting line-up. She will select a player for each of the five positions: center, right forward, left forward, right guard, left guard. However, there are only 3 of the 8 players who can play center. Otherwise, there are no restrictions. How many ways are there for her to select the starting line-up?

A basket contains 2 pink, 3 yellow, 8 red, and 1 black jelly beans. You grab a handful of 4 jelly beans. (a) How many groups of 4 jelly beans include exactly 1 of each color?   (b) How many groups of 4 jelly beans include at most 1 yellow?