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Suppose we want to choose 2 objects, without replacement, from the 3 objects pencil, eraser, and desk. (a) How many ways can this be done, if the order of the choices is taken into consideration? 25 0 How many ways can this be done, if the order of the choices is not taken into consideration? X

Suppose we want to choose 2 objects, without replacement, from the 3 objects pencil, eraser, and desk. (a) How many ways can this be done, if the order of the choices is taken into consideration? 25 0 How many ways can this be done, if the order of the choices is not taken into consideration? X

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Example Problem: Choosing 2 Objects from a Set Suppose we want to choose 2 objects, without replacement, from the 3 objects: pencil, eraser, and desk. #### (a) How many ways can this be done, if the order of the choices **is** taken into consideration? [ ] #### (b) How many ways can this be done, if the order of the choices **is not** taken into consideration? [ ] --- **Explanation:** - **Part (a)** asks us to consider the permutations of the objects, meaning the order in which we choose the objects matters. - **Part (b)** asks us to consider the combinations of the objects, meaning the order in which we choose the objects does not matter. When order **does** matter (permutations): - We can select any of the three objects first, and then select one of the remaining two objects. When order **does not** matter (combinations): - We are only concerned with distinct groups of two, regardless of their order.
Transcribed Image Text:### Example Problem: Choosing 2 Objects from a Set Suppose we want to choose 2 objects, without replacement, from the 3 objects: pencil, eraser, and desk. #### (a) How many ways can this be done, if the order of the choices **is** taken into consideration? [ ] #### (b) How many ways can this be done, if the order of the choices **is not** taken into consideration? [ ] --- **Explanation:** - **Part (a)** asks us to consider the permutations of the objects, meaning the order in which we choose the objects matters. - **Part (b)** asks us to consider the combinations of the objects, meaning the order in which we choose the objects does not matter. When order **does** matter (permutations): - We can select any of the three objects first, and then select one of the remaining two objects. When order **does not** matter (combinations): - We are only concerned with distinct groups of two, regardless of their order.
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