**General rule of counting**

If an event can be occured in *n*_{1} ways, and if that event is followed by other event which can be occured in *n*_{2} ways, if that two events are followed by the third event which can be occured in *n*_{3} ways, …. and so on, the that *k* continuing events can be occured in (*n _{1}×n_{2}×n_{3}×…×n_{k}*) ways.

**Example 4:**

In how many ways an organization can elect a leader, a secretary and a treasurer from their 10 members?

**Answer:**

Leader can chosen from the 10 members, means there are 10 ways to elect leader. After we get the leader, the (10-1)=9 members are left to be chosen as secretary, means there are 9 ways to elect secretary.

After we get leader and secretary, then (10-2)=8 members are left to be chosen as the treasurer, means there are 8 ways to chosen the treasurer. So, the ways to elect that three position =(10∙9∙8) ways =720 ways.

Notes: No matter what position which is chosen before the others, the number of ways to chosen is still teh same. Please investigated.

**Exercise Competency Test 4**

1. There are 4 chairs in a room. If there are 6 persons who will sit in that chairs, then the number of ways for them to sit at the chairs is equal to ….

A. 30 B. 120 C. 360 D. 720 E. 1440

Answer: C, explanation:

Suppose sitting in a series is important for permutation condition. Permutation will be explained so on. One person can not sit on two chairs. One person can sit on a chair only.

A. 96 B. 64 C. 48 D. 24 E. 12

Answer: C, explanation:

Numeral 0 can not fill room I.

The number of formation (based on position) which can be formed by the 4 runners are ….

A. 256 B. 32 C. 24 D. 16 E. 4

Answer: C, explanation:

=4×3×2×1=24

A. 125 B. 75 C. 60 D. 36 E. 24

Answer: D, explanation:

Each of the following numbers is more than three hundred (…>300). It means each numbers starts with {3,4,5}.

A. 125 B. 75 C. 60 D. 36 E. 24

Answer: A, explanation:

A. 360 B. 240 C. 120 D. 24 E. 10

Answer: A, explanation:

=6×5×4×3=360