introduction to counting techniques

Question 1

deals with the
occurrence of a random
event. It has been
introduced in Math to
predict how likely
events are to happen or
the measure of the
likelihood of an event to
occur.

Answer 1

probability

Question 2

How is probability
used to make
predictions

Answer 2

P(A) = number of favorable outcomes to A / total number of possible outcomes

Question 3

helps to organize and visualize
the different possible outcomes

• used to represent the
  probability of occurrence of
  events without using
  complicated formulas

Answer 3

tree diagram

Question 4

4 ways we can use tree diagram

Answer 4

• Brainstorming
  possible outcomes of
  a scenario
• Problem-solving
  and root-cause
  analysis
• Anticipating
  potential workflow
  issues
• Indicating
  hierarchy of tasks

Question 5

3 advantages of using tree diagram

Answer 5

• Better decision-
  making - Enhanced

troubleshooting

• Streamlined
  workflows

Question 6

Can we always use a tree diagram for organized counting?

Answer 6

Often we can use organized counting methods like
tree diagrams, lists, charts, and Venn diagrams to
help us count the possibilities in a given situation.

Question 7

If an event can occur in m different ways,
and another event can occur in n different
ways, then the total number of occurrences
of the events is m · n.

Answer 7

basic counting principle

Question 8

When do we use the counting principle?

Answer 8

When the choice that is to be made are independent of each other.

Question 9

How do you find the number of outcomes of an event?

Answer 9

You simply take the number of choices or possible
outcomes and then multiply them together.

Question 10

The product of all the positive integers
from n to 1, denoted by a special symbol
n! (read as “n factorial”).

Answer 10

factorial notation

Question 11

If n is a non-negative integer,
0! = ?

Answer 11

1

Question 12

n! = (n-1)! n where

Answer 12

n≥1.

Question 13

is an arrangement of objects in a specific order.

Answer 13

permutation

Question 14

When do we use the permutation?

Answer 14

Permutations are used when order/sequence
of arrangement is needed (where the order of

the data matters).

Question 15

Advantages or benefits of permutation

Answer 15

• To count the
  number of ways
  for determine
  arrangement
• Distinguishing
  for one
  arrangement to
  another
  arrangement
• To determine
  the number of
  sequence of
  letters and
  numbers

Question 16

Can we always use permutation for

organized counting?

Answer 16

No, because there are many Fundamental
Counting Principle problems that cannot be
solved with the permutation formula.

Question 17

formula for permutation if isa ra ka kuan given

Answer 17

nPn = n!

Question 18

formula for permutation if duha given

Answer 18

nPr = n!/(n-r)!

Question 19

n is the

Answer 19

total number of objects

Question 20

r is the

Answer 20

number of objects taken from n

Question 21

The number of permutations of n objects
taken n at a time where one object is
repeated S1 times, another is repeated
S2 times, and so on, is

Answer 21

permutation with repetition

Question 22

permutation with repetition formula

Answer 22

P = n!/s1!s2!s3!…sk!