Explain principle of multiplication with an example.
Answers
Step-by-step explanation:
In combinatorics, the rule of product or multiplication principle is a basic counting principle (a.k.a. the fundamental principle of counting). Stated simply, it is the idea that if there are ways of doing something and b ways of doing another thing, then there are a · b ways of performing both actions. In this example, the rule says: multiply 3 by 2, getting 6.
The sets {A, B, C} and {X, Y} in this example are disjoint sets, but that is not necessary. The number of ways to choose a member of {A, B, C}, and then to do so again, in effect choosing an ordered pair each of whose components are in {A, B, C}, is 3 × 3 = 9.
As another example, when you decide to order pizza, you must first choose the type of crust: a thin or deep dish (2 choices). Next, you choose one topping: cheese, pepperoni, or sausage (3 choices).
Using the rule of product, you know that there are 2 × 3 = 6 possible combinations of ordering a pizza.
Another typical example is using it with the rule of sum, in this case, we have two groups, p A with 3 elements and p B with 10 elements. We want to pick one element ( we don't care if it is from group A or B) and a second element that must be from p B. The way that we can choosethe elements are:
{\displaystyle \mathrm {Total} \ \mathrm {ways} =(3*10)+(10*9)}
First, we use the rule of product to get the number of ways if we pick ann element from group A and then from group B. After this, we repeat the process but now changing the element of group A by element of group B and multiply by the number of elements S in B - 1 because we pick one of this.
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MULTIPLICATION PRINCIPLE
Multiplying (or dividing) the same non-zero number to both sides of an equation does not change its solution set.
Example:
so if 6x = 12, then 18x = 36 for the same value of x (which in this case is x = 2).
The way we use the multiplication principle to solve equations is that it allows us to isolate the variable by getting rid of a factor that is multiplying the variable.
Example: 2x = 6
To get rid of the 2 that is multiplying the x, we can divide both sides of the equation by 2, or multiply by its reciprocal (one-half).
Either divide both sides by 2:
Example: 2x = 6
To get rid of the 2 that is multiplying the x, we can divide both sides of the equation by 2, or multiply by its reciprocal (one-half).
Either divide both sides by 2:
or multiply both sides by a half:
Whether you prefer to think of it as dividing by the number or multiplying by its reciprocal is not important, although when the coefficient is a fraction it is easier to multiply by the reciprocal:
Example:
Multiply both sides by the reciprocal of the coefficient, or