When some objects are randomly selected, which of the following is true? Multiple Choice The order in which objects are selected does not matter in combinations. The order in which objects are selected matters in both permutations and combinations. The order in which objects are selected matters in combinations. The order in which objects are selected does not matter in permutations.
Question
When some objects are randomly selected, which of the following is true?
Multiple Choice
The order in which objects are selected does not matter in combinations.
The order in which objects are selected matters in both permutations and combinations.
The order in which objects are selected matters in combinations.
The order in which objects are selected does not matter in permutations.
Solution
The correct answer is: The order in which objects are selected does not matter in combinations.
Here's why:
-
In mathematics, there are two ways to count or "arrange" different objects: permutations and combinations.
-
A permutation is an arrangement of objects where the order is important. For example, if you have three books (A, B, and C), there are six different ways to arrange them (ABC, ACB, BAC, BCA, CAB, CBA). Each arrangement is a different permutation.
-
A combination, on the other hand, is an arrangement of objects where the order is not important. Using the same three books (A, B, and C), there is only one way to combine them. Whether you arrange them as ABC, ACB, BAC, BCA, CAB, or CBA, they are considered the same combination because they contain the same books.
So, the statement "The order in which objects are selected does not matter in combinations" is true.
Similar Questions
Which of the following best describes combination?Group of answer choicesorder of the objects does mattercounting principles are appliedsame results occurs when positions of objects are switcheddifferent results occurs when positions of objects are switched
In a lottery daily game, a player picks four numbers from 0 to 9 (without repetition). How many different choices does the player havea) If order matters? b) If order does not matter?
Suppose we want to choose 4 objects, without replacement, from 18 distinct objects.(If necessary, consult a list of formulas.)(a) How many ways can this be done, if the order of the choices does not matter?(b) How many ways can this be done, if the order of the choices matters?
There are 12 paintings at an art show. Three of them are chosen randomly to display in the gallery window. The order in which they are chosen does not matter. How many ways are there to choose the paintings?A.220B.144C.1320D.36SUBMITarrow_backPREVIOUS
Suppose we want to choose 6 objects, without replacement, from 10 distinct objects.(If necessary, consult a list of formulas.)(a) How many ways can this be done, if the order of the choices does not matter?(b) How many ways can this be done, if the order of the choices matters?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.