What multiplication fact is illustrated in each these diagrams? Name the multiplication model that is illustrated. Complete parts (a) through (d). (a) ** ** * *
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
 alt="### Multiplication Models and Facts
**10. What multiplication fact is illustrated in each of these diagrams? Name the multiplication model that is illustrated. Complete parts (a) through (c).**
#### (a)
**Diagram:**
This diagram displays three circles, each containing five stars.
- **What multiplication fact is illustrated in the diagram above?**
____________ (Type an equation.)
- **What multiplication model is illustrated?**
- Rectangular area model
- Number-line model
- Multiplication tree model
- Set model
---
#### (b)
**Diagram:**
This diagram is a grid composed of four rows and seven columns, making a total of 28 squares.
- **What multiplication fact is illustrated in the diagram above?**
____________ (Type an equation.)
- **What multiplication model is illustrated?**
- Rectangular area model
- Number-line model
- Set model
- Multiplication tree model
---
#### (c)
**Diagram:**
This diagram shows a number line with jumps labeled from 0 to 12. There are three equal jumps of four steps each, marked by curved arrows.
- **What multiplication fact is illustrated in the diagram above?**
____________ (Type an equation.)
- **What multiplication model is illustrated?**
- Rectangular area model
- Set model
---
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