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A. Selecting 2 songs from 10 choices for an audition piece. B. Fixing the schedule of a group of students who must take exactly 8 subjects.
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Department of Education
Quarter 3 - Module 3:
Z est for P rogress Z eal of P artnership
Name of Learner: ___________________________
Grade & Section: ___________________________
Name of School: ___________________________
What I Need to Know
The module contains only one lesson: Lesson 3 - Illustrate combination of objects. Lesson 4 - Differentiate permutation from combination of n objects taken r at a time.
In this module, you are expected to: a. Define and illustrate combination of objects. b. Differentiate permutation from combination of n objects taken r at a time. c. Relate combination in real life situation.
What I Know
Choose the letter of the correct answer. Write your answer on the space provided.
_____ 1. What do you call to the selection of objects regardless of their order? A. combination C. integration B. differentiation D. permutation
_____ 2. How many ways can a code be formed from the digits 0 to 9 if a combination lock must contain 5 different digits? A. 15 120 B. 30 240 C. 151 200 D. 1 000 000
_____ 3. Which of the following situations does NOT illustrate combination? A. Selecting 2 songs from 10 choices for an audition piece. B. Fixing the schedule of a group of students who must take exactly 8 subjects. C. Enumerating the subsets of a set D. Identifying the lines formed by connecting some given points on a plane.
_____ 4. What is C (10, 4)? A. 210 B. 200 C. 220 D. 230
_____ 5. From 10 participants in a virtual orientation of Reginal Writers in Mathematics 10, 4 will be chosen to lead in each group. In how many ways can the participants be chosen? A. 24 B. 210 C. 5,040 D. 24 720
What is it
Troop Leader A: shakes hand with B, then with C, D, E, and F. the total handshakes made by troop leader A is 5;
Troop Leader B: shakes hand with C, then D, E and F. B did not shake hand with A since the handshake between A and B is the same as between B and A (Order is NOT important).
Troop Leader C: made 3 handshakes with D, E, and F.
Troop Leader D: made two handshakes with E and F.
Troop Leader F; make 1 handshake with F.
Total Number of handshakes is 15.
Combination refers to the selection of objects where order is not important. That is, changing the order of the objects does not create a new combination.
For instance, the 3 combinations of the 3 letters T , I , and N taken 2 at a time are: TI , TN , and IN
TI and IN are considered one combination. Similarly, IN and NI and TN and NT are the same combinations.
There is only one combination that can be made from the letters T , I , and N taken 3 at a time. That is TIN
TIN , TNI , INT , NIT , ITN , and NTI are considered one combination.
The combination of n things or objects taken r at a time can be denoted by
C(n,r).
How does combination differ from permutation?
xa mpl e 1
a. Your locker code is 543, if you enter 435 it won’t open because it is a different ordering. Try to observe the table below.
Basic Comparison Permutation Combination
Meaning
Permutation refers to the different ways of arranging a set of objects in sequential order.
A combination refers to several ways of selecting items from a large set of objects, such that their order does not matters.
Order Important
Order matters
Not important
Doesn’t matter
Denotes Arrangement Selecting
Question
How many different arrangements can be created from a given set of objects?
How many different groups can be chosen from a larger group of objects?
Formula/Notation
nPr =^ ( )
P(n,r), Pn,r or
nCr = (^) ( )
C(n,r), C n,r or
Order does matter (Permutation)
Order doesn’t matter (Combination) 543
Example 3
a. How many ways can 8 students be seated for a selfie if only 4 seats are available?
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Solution:
There are 8 students to choose from, first seat can be filled in 8 ways. The occupant of the 2nd^ seat can be chosen from the 7 students. Thus, the second seat can be filled in 7 ways. After the first two seats are filled, the third and fourth seats can be filled using the same reasoning, in 6 and 5 ways, respectively.
P(n,r) = (^) ( )
b. Suppose you are given an ordinary deck of playing cards. In how many was can 5 cards be selected?
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The number of ways of selecting r objects taken from n distinct objects where arrangement is not important.
C(n,r) = (^) ( )
Solution: Selecting 5 cards from a deck of cards is a problem on selecting 5 objects taken from 52 distinct objects where arrangement is not important. Thus, n = 52, and r = 5, and
C(n,r) = (^) )
c. RRJ apparel is on 50% sale. If you are to select 2 shirts and 2 jeans of which there 8 designs for shirts and 6 different kinds of jeans, how many combinations do you have?
C(n,r) = (^) ( ) C(n,r) = (^) ( )
“ and ” means multiply
“ or ” mean add
and 2 vowels can be formed?
PATTERN A = hundreds place value of number 3 answer B = ones place value of answer in number 4 C = ten thousands value of answer in number 2 D = ones place value in number 1
What I Can Do
It’s your time to shine
Assessment
Choose the letter of the correct answer. Please write your answer on the space provided.
_____1. What is the expanded form of (^) 10 C 2?
A. C(10, 2) =( ) C. C(10, 2) = (^) ( )
_____2. What term refers to several ways of selecting items from a large set of objects, such that their order does not matter? A. combination C. integration B. differentiation D. permutation
_____ 3. Which of the following experiments will determine that order is NOT important? A. Selecting the top 3 winners in Math Quiz Bowl. B. Setting a 4-digit code in a vault. C. Buying 3 out 7 designs of face mask. D. Assembling a jigsaw puzzle.
_____4. What is the correct answer if you will solve C(5,2)? A. 10 B. 60 C. 20 D. 120
_____5. How many ways of selecting 3 flavors of ice cream can you make if there are 6 flavors available? A. 15 B. 20 C. 30 D. 40
_____6. How many ways can 5 cars be parked if there are 7 available parking spaces? A. 1260 B. 1540 C. 2230 D. 2520
_____7. In how many combinations can Coco have in the 5 displays of chicken inasal with unlimited rice? A. 1 B. 5 C. 10 D. 120
_____8. How many different words can we make from the letters L, O, V, and E? this assumes every possible combination is a word. A. 2 B. 6 C. 12 D. 24
_____9. At the grocery section, Kyvhan wanted to select 2 diapers, 2 milks, 3 shampoos.
In how many different selections does he have if there 5 diapers and 4 milks and 5 shampoos displayed? A. 30 B. 50 C. 80 D. 120
_____10. How many ways can Cheem invites 3 or more friends to her birthday party if she has on 5 friends? A. 5 B. 10 C. 16 D. 50
