Answer to Question #98143 in Statistics and Probability for C

Question

Please explain to me the counting principle in probability,what does factorials mean and why do we sometimes divide factorials?Please explain all the rules of counting principles with simple examples and when must I use which rule please?

Answer 1

Fundamental counting Principle :

Let E₁ and E₂ are two events. The first event E₁ happens in "m" different ways,. After the happening of E_1, the event E₂ happens in n different ways.

The number of ways that the two events can happens is m $\times$ n

This principle can be extended to three or more events.

Factorial means:

Factorial means the product of an integer and all integers below that required number.

Example:

$$4! = 4 \times 3 \times 2 \times 1$$

we sometimes divide factorials: When we are trying to find the combinations or permutations, we can use to divide the factorial.

Example:

$$\binom {n} {r } = \frac {n!}{(n-r)! r!}$$

Examples for counting Principle:

(1). If we have 3 shirts and 4 pants, the number of ways wearing these shirt and pant combination is 4 x 3 = 12 ways

(2). There is three cities A, B and C, number of routs from city A to city B is 3 and city B to C is 4 ways.

Total number of ways to go from city A to city B = 3 x 4 = 12

Fundamental Rules

we can use the fundamental rule of multiplication, if we have independent events.

We can use the fundamental rule of addition, if we have dependent events.