**Definition of Combination**

The number of combination of *k* elements which are taken from *n* elements which are provided is

combination formula

Example 12:

a. A Foundation will send 3 messengers to get to a conference. If those three messengers are chosen from the 8 candidates that satisfy, determine the number of ways of the foundation to select the three messengers.

b. In a room, there are 10 persons who shake hands each other, determine the number of shake hand occurred.

Answer:

a. Three persons are chosen from 8 persons. The number of ways to determine the three messengers is equal to the number of combination of 3 persons taken from 8 persons, which is

b. Ten persons shake hand each other. The number of hand shaking are occured is equal to the combination of 2 which is taken from10, is:

**Exercise Competency Test 12**

1. A company will choose 4 employees from 10 persons who pass the test. The number of ways the company to choose that 4 persons is equal to …

A. 5400 B. 5040 C. 420 D. 210 E. 105

Answer: D, Explanation:

2. A football competition is joined by 12 teams. At the first round, each team has to compete another. The number of matches at the 1^{st} round is equal to ….

A. 132 B. 66 C. 33 D. 24 E. 12

Answer: B, Explanation:

Each match just consist ot two teams. Duel.

3. On a circle there are 8 different points. By using the 8 points then the number of bowstring which can be made = …

A. 56 B. 28 C. 16 D. 14 E. 8

Answer: B, Explanation:

Its axiom: A bowstring can be made by two points on a circle

Bowstrings are {AB,AC,…,GH}→

_{8}C

_{2}.

AC≡ABC

⋯

BH≡⋯≡BCDEFGH

the number of bowstring which can be made =

_{8}C

_{2}

4. A student wants to do a test, he has to answer 7 from the 10 problems are provided. The number of ways to choose the problem to be solved = …

A. 120 B. 110 C. 90 D. 80 E. 70

Answer: A, Explanation:

5. In a employee selection of a company, 5 male and 4 female pass the test as the candidate. If the company only needs 2 male, and 2 female, then the number of ways for the company to choose the employee is equal to …

A. 3024 B. 720 C. 240 D. 120 E. 60

Answer: E, Explanation:

6. In a bag there are 7 red marbles and 4 white marbles. Will be taken 4 marbles. The number of ways to take 2 red marbles and 2 white marbles =…

A. 504 B. 252 C. 126 D. 63 E. 27

Answer: C, Explanation: