Week
4
Combinations
LESSON 1 Illustrating the Combination of Objects
THINGS TO REMEMBER
A combination is the number of ways of selecting from a set when the order is not important.
LET’S DO THIS
Aside from beautiful places, Zamboanga del Sur is also known for its pasalubong items.
Rowena’s offers different tarts: (Buko, Ube, Pineapple, Yema and Mango). A box of tart contains 9
pieces and you are allowed to have a maximum of three different flavors per box, how many different
combinations are there?
a. There is only one flavor
Solution:
How many flavors are there?
_______________________
b. There are two flavors.
Solution:
How many different flavors can you pair with Buko?
____________________________
How many different flavors can you pair with Ube?
____________________________
How many combinations of two flavors are there?
_____________________________
c. There are three flavors
Solution:
How many different flavors can you pair with Ube?
______________________________
How many different flavors can you pair with Pineapple and Ube?
______________________________
How many different flavors can you pair with Ube and Mango?
_____________________________
How many combinations of three different flavors are there?
_____________________________
I CAN DO THIS!
You want to surprise your mother on her birthday by preparing a fruit salad. You went to
Tambulig market to buy ingredients (pineapple, papaya, banana, and buko). Due to limited budget
and you still want to give your mother a present, you are opted to buy only 3 different fruits. List all
possible combinations.
Answer: ________
LESSON 2 Combination taken r at a time
THINGS TO REMEMBER
A combination is the choice of r things from a set of n things without replacement and where
order does not matter
n! n!
C (n, r) = . or nCr = .
r ! ( n−r ) ! r ! ( n−r ) !
Remember:
n → total
r → want
LET’S DO THIS
Supply the missing parts for the correct solution.
1. 4C3
4!
SOLUTION: C (4, 3) =
3! ( 4−3 ) !
4! 4 • 3• 2•1
C (4, 3) = =
3! 1 ! 3 •2 •1 •1
C (4, 3) = ¿¿
C (4, 3) = ¿¿
2. 6C2
6!
SOLUTION: C (6, 2) =
2! ( 6−2 ) !
6! 63•5 •4 •3 •2 •1
C (6, 2) = =
2! 4 ! 2 •1• 4 • 3• 2•1
C (6, 2) = ¿¿
C (6, 2) = ¿¿
3. 12C5
12!
SOLUTION: C (12, 5) =
5! (12−5 ) !
12 ! 12•11 • 10• 9 •8 •7 •6 • 5• 4 • 3• 2• 1
C (12, 5) = =
5! 7 ! 5 • 4 •3 •2 •1• 7 •6 •5 • 4 •3 •2 •1
C (12, 5) = ¿¿ •¿
C (12, 5) = ¿¿
I CAN DO THIS
There are 12 boys and 14 girls in Mrs. Dela Cruz’s Math class. Find the number of ways Mrs.
Dela Cruz can select a team of 3 students from the class to work on a group project. The team is to
consist of 1 girl and 2 boys.
For boys: For girls:
SOLUTION: n = 12, r = ___ n = ___, r = 1
12 ! ¿¿ !
C (12, __) = C (___, 1) =
¿! ¿ ¿ 1! ( ¿ ¿−1 ) !
12! ¿¿ !
C (12, __) = C (___, 1) =
¿¿ !¿ 1! ¿
❑
C (12, __) = C (___, 1) =
C (12, __) = ¿¿ C (___, 1) = ¿¿
EVALUATION
A. Solve each problem. Each item is 5 points each.
1. If there are seven barangays in Tambulig competing for inter-barangay basketball league and
each team must play every other team in the eliminations, how many possible games in each
team meet.
2. Suppose you are the owner of a sari-sari store and you have 8 pieces of different canned
sardines (Ligo, 555, Mega, Young’s Town, Mariko, Swan, Atami, and King Cup) and you are
only allowed to display 7 canned goods on the shelf, how many possible combinations are
there?
3. Teacher Jay selected 8 students in the entire Grade 10 to represent in Math culminating
activity. How many ways can Teacher Jay select 2 students to work in the activity?
B. Encircle the letter of your answer.
1. Which of the following situations can be solved using cannot be solved using combination?
a. buying fruits from the fruit stand b. selecting the dress to wear
c. arranging the books in a shelf d. choosing the movies to watch
2. Which of the following situations can be solved using combination?
a. Falling in line for the flag ceremony. b. Choosing your classmates to invite in the party.
c. Aligning the potted plants along the window. d. Stacking the cards in the deck.
3. Which of the following situations does NOT illustrate combination?
a. displaying the trophies in a shelf b. ranking the students according to academic grades
c. listing the Harry Potter installments d. buying the ingredients for Bicol Express
4. Which of the following situations involving combinations has 924 ways of happening?
a. picking 6 balls from a basket of 12 balls
b. determining the top three winners in a Science Quiz Bee
c. forming different triangles out of 5 points on a plane, no three of which are collinear
d. forming triangles from 7 given points with no three of which are collinear
5. Janice wanted to buy 12 different round fruits in order to achieve the complete set of round fruit
platter as part of the New Year’s Day celebration, but can only afford to buy 9 different types.
How many possible combinations can she choose from?
a. 100 b. 120 c. 200 d. 220
EVALUATION
Solve each item. Write your answers on the answer sheet provided.
1. C (8, 3) = ___
2. C (___, 4) = 15
3. C (8, ___) = 28
4. C (9, 9) = ___
5. C (___, 3) = 35
6. C (10, ___) = 120
7. C (___, 2) = 78
8. C (11, ___) = 165
9. C (8, 6) = ___
10. C (14,10) = ___
Week Word Problems Involving
5 Permutations and Combination
THINGS TO REMEMBER
Combination is the number of ways of selecting from a set when the order is not important.
Combination is the number of ways of selecting from a set when the order is not important.
The number of combinations of n objects taken r at a time is given by nCr = n! / (n- r)! r! , n ≥ r.
Permutation refers to the different possible arrangement of sets of objects.
Permutations refers to the different possible arrangements of a set of objects. The number of
permutations of n objects taken r at a time is nPr = n!/ (n – r)!, n≥ r.
The basic difference between a combination and a permutation is that while the former is just a
way of selecting something, the latter is a way of selecting as well as arranging it.
LET’S DO THIS
At Dexter’s Pizza Parlor there are three different toppings (all meat, pepperoni, shawarma) to
choose from, where a costumer can order any number of these toppings. If you dine in a said pizza
parlor, with how many possible toppings can you actually order your pizza?
Solutions:
6+
a. How many pizzas are there with only one topping? List down all answer.
(___,___,___)=______ number of pizzas.
b. How many pizzas are there with only two toppings? List down all answer.
(___,___,___)=______ number of pizzas.
c. How many pizzas are there with only three toppings? List down all answer.
(___,___,___)=______ number of pizzas.
Therefore there are ________ combinations of toppings in Dexter’s Pizza Parlor.
I CAN DO THIS
WHO AM I?
Identify which situations illustrate permutation and which illustrate combination, then solve.
Check if
SITUATIONS ANSWER
Permutation Combination
1. Determine the top three winners from 10
contestant in a mathematics quiz bee.
2. Choosing 2 household chores to do before
dinner from 5 different chores.
3. Forming a committee of 4 members from 5
people.
4. Four people posting picture in a row.
5. Forming different committees of 4 people
from a pool of 7 people.
LET’S DO MORE
SOLVE THIS!
1. Let us say there are three flavors of ice cream: cheese, chocolate and vanilla. We can
have two scoops. How many variations will there be?
ANSWER: _______
2. In how many ways can 6 students be seated in a row of 6 seats if 2 of the students insist
on sitting beside each other?
ANSWER: _______
3. At Cheekies Pizza Parlor, there are seven different topping, where a costumer can order
any number of these toppings. If you dine at the said pizza parlor, with how many possible
set of toppings can you actually order your pizza?
ANSWER: _______
4. There are 8 basketball teams competing for the top 4 standings in order to move up to the
semi – finals. Find the number of possible rankings of the four top teams?
ANSWER: _______
LET’S DO THIS
Solve the following permutation and combination problems.
1. What is the number of permutation of 9 objects taken 3 at a time?
2. The covered walk of a school is to be lined with flags. How many different arrangements are
there of the 10 flags if 5 are blue, 3 are red and 2 are white?
3. How many different committees of 5 people can be formed from a pool of 9 people?
4. In a 10 – item Mathematics problem- solving test, how many ways can you select 5 problems
to solve?
5. In how many ways can a team consisting of 2 boys and 3 girls be formed if there are 6 boys
and 10 girls who qualified to be a team?
EVALUATION
Check the following situations if permutation or combination, then solve.
Check if
SITUATIONS ANSWER
P C
1. In how many ways can seven students be arranged in a line?
2. If your school canteen offers pork, beef, chicken, and fish for
main dish, chop suey, pinakbet, and laing for vegetables dishes,
banana 23 and pineapple for dessert, and tea, juice , and
softdrinks for beverage, In how many ways can you choose your
meal consisting of 1cup of rice, 1main dish, 1 vegetables dish, 1
beverage , and 1 dessert.
3. Rabin has 9 mathematics books and 5 science books. The shelf
has space for only 7 books. If the first four positions are to be
occupied by mathematics books and the last three by science
books, in how many ways can this be done?.
4. In how many ways can 4 people be seated around a circular
table?
5. A box contains 6 red balls and 4 blue balls. Three balls are
drawn at random. In how many ways can the 3 balls be drawn
from 10 balls?
NAME : ____________________________________ YEAR/SECTION : ________________
MATHEMATICS, 3rd QUARTER, WEEK 4
ANSWER SHEET
TEACHER’S REMARKS: __________________________________________________________
NAME : ____________________________________ YEAR/SECTION : ________________
MATHEMATICS, 3rd QUARTER, WEEK 4
SOLUTION SHEET
.
NAME : ____________________________________ YEAR/SECTION : ________________
MATHEMATICS, 3rd QUARTER, WEEK 5
ANSWER SHEET
TEACHER’S REMARKS: __________________________________________________________
NAME : ____________________________________ YEAR/SECTION : ________________
MATHEMATICS, 3rd QUARTER, WEEK 5
SOLUTION SHEET
.
