(a) How many different groups of 6 people could be selected from a group of 24 to go on a trip? groups (b) How many groups of 18 could be selected from a group of 24? groups (c) Your answers in parts (a) and (b) should have been the same. Explain why this is true. The answers are ---Select--- the same not the same because selecting 6 people to go on a trip is ---Select--- the same not the same as selecting to stay behind.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
The factorial function occurs often in probability and statistics. For a non-negative integer n, the factorial is denoted n! (which is read "n factorial") and is defined as follows: First, 0! is defined to be 1. Next, if n is 1 or larger then n! means
Thus
Consult the Technology Guide to see how to enter the factorial operation on the calculator.
In many counting situations, the number of possibilities is not affected by order. For example, if a group of 6 people is selected from a group of 24 to go on a trip, then the order of selection does not matter. In general, the number C of ways to select a group of k things from a group of n things is given by
| n! |
| k!(n − k)! |
if k is not greater than n.
groups
(b) How many groups of 18 could be selected from a group of 24?
groups
(c) Your answers in parts (a) and (b) should have been the same. Explain why this is true.
(d) What group size chosen from among 24 people will result in the largest number of possibilities?
people
How many possibilities are there for this group size?
possibilities
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