Permutation and Combination - PPT

1. Permutation

2. Permutation is an arrangement of a number of objectsin a
definite order.
Order is important.
A, B and C
How many possible arrangements are there?
AB AC BC
BA CA CB
6 possible arrangements

7. Example 5
How many 4-letter words can be formed from the
letters in the word MOBILE?
Solution
n = 6 P(6,4) = 6 • 5 • 4 •
3
r = 4 = 360

8. Permutation using EXCEL
= PERMUT (n , r)

10. Combination

11. A combination refers to a selection of items
from a larger set, where the order of the
selected items does not matter.

13. How many ways can we choose 3 students from 6?
Solution:
n = 6
r = 3

14. So, the number of ways to choose 3 students from 6,
where order doesn't matter, is 20
n = 10
r = 4

15. How many ways can a principal choose 3 from 30 teachers to
attend a conference abroad?

16. Combination using EXCEL
= COMBIN (n , r)

17. How many ways can a principal choose 3 from 30 teachers to
attend a conference abroad?

18. Feature Permutation Combination
Definition
An arrangement of objects in a
specific order.
A selection of objects without
regard to order.
Order Matters?
Yes, order is important in
permutations.
No, order does not matter in
combinations.
Formula
Example
How many different ways can 3
people be seated in 5 chairs?
How many ways can 3 people be
selected from 5 to form a team?
Use Case
Used when arranging items or
people.
Used when selecting items or
people.
Result
Interpretation
Permutations tell us how many
different orders are possible.
Combinations tell us how many
different groups can be made.
Permutation vs Combination: Key Differences

19. Permutation & Combination
•In probability, permutation and combination are often
used to calculate the total number of possible outcomes
and favorable outcomes, which help in determining the
likelihood of certain events.
•In statistics, combinations are used in analyzing
possible sample selections or subsets of data, while
permutations are used in calculating various test
statistics.
•Permutation and combination are used in a variety of
real-world scenarios, such as seating arrangements,
scheduling works, and even in planning and organizing
events or competitions.

20. Let’s Try!
Permutation and Combination:
https://forms.gle/QFKX6tXCnKNyYh3L6

21. Let’s Try!
1. How many different ways can 4 students be arranged in a row from a group of 7 students?
A) 7!
B) P(7,4) =7! / 3!
C) C(7,4)=7! / 4!3!
D) 7 × 6 × 5 × 4
2. In how many ways can a president, vice-president, and secretary be selected from a group of 10
people?
E) C(10,3)
F) P(10,3)
G) 10!
H) 10 × 9 × 8

22. Let’s Try!
3. How many ways can a 5-member team be selected from a group of 12 people?
A) C (12,5)
B) P (12,5)
C) 12 × 11 × 10 × 9 × 8
D) 12!
4. How many ways can 3 prizes be awarded to 10 students if each student can win only one prize and
the order of the prizes matters?
E) C (10,3)
F) P (10,3)
G) 10 × 9 × 8
H) 10!

23. Please show your computation for the following:
5-7. How many different 4-digit numbers can be formed
using the digits 2, 4, 5, 6, 7, and 8 if no digit is repeated?
8-10. How many ways can a 3-person team be chosen
from 6 people, where the order of selection does not
matter?