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EXAMPLES NOT WRITTEN ON THE BOARD:
PERMUTATIONS AND COMBINATIONS
5. Find the number of ways in which 6 teachers can be can be assigned to 4 sections if no
teacher is assigned more than one room. (Ans: 360)
6. How many ways can 1 president, 1 vice president and 1 secretary be chosen from 14
PICE members? (Ans: 2,184)
7. How many different permutations can be made of the letters in the word infinity? (Ans:
3,360)
8. A signal is formed by arranging 6 flags in a vertical line. How many signals can you form
from 4 identical blue flags and 2 identical violet flags? (Ans: 15)
9. How many ways can 7 people be assigned to 1 triple and double rooms? (Ans: 210)
PROBABILITY
1. Draw a card from a well-shuffled deck of cards. Determine the probability that the card
drawn is a two or a face card. (Ans: 4/13)
2. A single 6-sided die is rolled. What is the probability of rolling a 2 or a 5? (Ans: 1/3)
3. A spinner has 4 equal sectors colored yellow, blue, green and red. What is the
probability of landing on a red or blue after spinning the spinner? (Ans: ½)
4. Draw a card from a well-shuffled deck of cards. Determine the probability of drawing a
red or an ace? (Ans: 7/13)
5. A single card is chosen at random from a standard deck of 52 playing cards. What is the
probability of choosing a king or club? (Ans: 4/13)
ASSIGNMENT
INSTRUCTION: Provide a complete and neat solution for the following problems on a one
whole sheet of short bond paper. (Oo, pwedeng magsulat sa likod.)
DUE: February 18, 2020 (Tuesday)
I. PERMUTATIONS AND COMBINATIONS
1. The HR Manager of Ayala Land Corporation is to hire 3 out of 10 equally qualified

applicants. How many ways can the manager choose?
2. Of 12 points on a plane, no 3 points lie on the same line except 5 points which all belong
to the same line. How many lines can be determined by these 12 points?
3. How many diagonals can you form in a polygon of n sides?
4. In how many ways can you color a poster if there are 5 different colors available?
5. In how many different ways can you arrange 4 identical Algebra books, 1 Calculus book
and 3 identical Mechanics book in a shelf by taking all the books in each arrangement?
6. In how many ways can the books in Math, Hydraulics and Structural Engineering be
arranged on a shelf if Math has 3 volumes, Hydraulics has 2 volumes and Structural
Engineering has 4 volumes?
7.
a. If repetitions are not permitted, how many 3-digit numbers can be formed from
the digits 1, 2, 4, 5, 7, 8 and 9?
b. How many different 4-digit integers can be formed if they are to be greater than
6000?
c. How many different numbers can be formed from the given integers if they are
to be greater than 900000 and of different digits?
8. There are 6 people lining up to pay telephone bills. If two persons don’t want to follow
each other, how many different line-ups are possible?
9. In how many ways can 5 engineers and 4 nurses be arranged in a round table if the
nurses insisted to be sitting side by side?
10. There are 36 lines that can be drawn from an n-cornered convex polygon. How many
corners are there in all?
11. In how many ways can a panel of 5 judges declare a winner in a beauty contest?
12. Four married couples have bought 8 seats in a row for a Ben & Ben Concert. In how
many different ways can they be seated
a. with no restrictions?
b. if each couple is to sit together?
c. if all men sit together to the right of all women?
II. PROBABILITY
1. A die is loaded in such a way that an even number is twice as likely to occur as an odd
number. Find the probability that if this die is rolled, a number less than 4 occurs.
2. A coin is tossed twice. What is the probability that at least one head occurs.
3. A certain statistical observation found that it has a probability of failing once equal to
0.422, twice equal to 0.141 and thrice equal to 0.016. Determine the probability that it
will fail once or thrice.
4. A real estate agent has 8 master keys to open several homes. Only 1 master key will
open any given house. If 40% of these homes are usually left unlocked, what is the
probability that the real estate agent can get into a specific home if the agent selects 3
master keys at random before leaving the office?
5. One bag contains 4 white balls and 3 black balls and a second bag contains 3 white balls
and 5 black balls. One ball is drawn at random from the second box and is placed unseen
in the first bag. What is the probability that a ball now drawn from the first bag is black?
6. In a poker hand consisting of 5 cards, what is the probability that all 5 are diamonds?
(diamond flush)
7. The probability that a doctor correctly diagnoses COVID-19 is 0.7. Given that the doctor
makes an incorrect diagnosis, the probability that the patient enters a law suit is 0.9.
What is the probability that the doctor makes an incorrect diagnosis and the patient
sues?
8. The probability that an automobile being filled with gasoline will also need an oil change
is 0.25; the probability that it needs a new oil filter is 0.40; and the probability that both
the oil and filter need changing is 0.14.
a. If the oil had to be changed, what is the probability that a new oil filter is needed
b. If a new oil filter is needed, what is the probability that the oil has to be
changed?

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EXAMPLES NOT WRITTEN ON THE BOARD:

PERMUTATIONS AND COMBINATIONS

DUE: February 18, 2020 (Tuesday)

I. PERMUTATIONS AND COMBINATIONS

1. The HR Manager of Ayala Land Corporation is to hire 3 out of 10 equally qualified

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