Fundamental Principle of Counting, an introduction to probability

Fundamental Principle of Multiplication
Fundamental Principle of Counting is often called rule of counting. The rule of counting is method of counting the number of members of an event without firstly register the whole members of that event. The calculating of the number of members of event by using the rule of counting can be based on tree diagrams method which is explained above.

Pay attention to example 2 above. By using tree diagram we can see that: the hundreds can only be occupied by numeral of 2 (means that there is only 1 way to determine the hundreds numeral), by using number 2 then there are 4 numbers remainder which can be used to occupy tens numeral (means that there are 4 ways to determine the tens numeral). Next, since 2 numbers has been used for the hunders and tens then there are 3 numbers remainder which can be used to occupy the units numeral (means that there are 3 ways to determine units numeral). So, the number of numeral which can be formed is equal to: 1×4×3=12.

Rule of counting:
If an event can occur in m ways, And if that event is followed by other event which can occur in n ways, then that two events can occur in m×n ways.

a. City A and B are connected by three different roads, and city B and C are connected by 2 different roads. If Amat starts his trip from city A, how many ways which he can choose to get city C?
b. Ali has 5 shirts and 3 pants. How many ways which Ali can choose to make pairs of this shirts and pants?
Answer:
a. From City A to city B there are three roads. From B to C there are 2 roads. The ways to get to city C from city A =3×2 ways =6 ways. Show on the following figure that the six ways.

path
path

{ad,ae,bd,be,cd,ce}
b. The number of shirts =5; the number of pants =3. The number of way to make pairs of shirts and pants =5×3=15 way.
Exercise Competency Test 3
1. There are 6 roads which connect city A and city B and there are 4 roads which connect city B and C. If someone wants to get to city C from A, then the number of possible ways which can be got is ….
A. 10 B. 12 C. 14 D. 24 E. 48
Answer: D, explanation:

6×4=24
2. Bobi has 6 shirts and 3 ties. The number of way to make pairs of his shirts and ties is ….
A. 9 B. 12 C. 15 D. 18 E. 21
Answer: D, explanation:

6×3=18
3. In the election of chairman and secretary in an organization there are 4 candidates of the chairman, and 3 candidates for the secretary. The number of way to make pairs of the chairman and the secretary by using these candidates is ….
A. 7 B. 8 C. 12 D. 16 E. 25
Answer: C, explanation:

4×3=12
4. The numbers which consist of 2 digits of different numeral which will be formed with the numerals: 1, 2, 3, 4, 5, 6. The number of numbers that can be formed is ….
A. 64 B. 32 C. 30 D. 18 E.16
Answer: C, explanation:

array of all numbers expected
array of all numbers expected

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