Combination Formula – Multiple Choice Questions

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

combination formula
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

persons

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:
persons shake

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:

employee combination

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 1st 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.

number of matches

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

bowstring

Bowstrings are {AB,AC,…,GH}→8C2.
AB≡BA
AC≡ABC

BH≡⋯≡BCDEFGH

the number of bowstring which can be made = 8C2
bowstring combination

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:

problems combination

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:

candidate combination

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:

taken marbles

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