Welcome to my presentation

Presentation on counting method: permutation & combination

Presenting to Dr. professor. Shwkat ali

Presenter : ANAMUL HAQUEID: 16012042

Permutations and CombinationsAn arrangement or listing in which order or placement is important is called apermutation.

Simple example: “combination lock”

31 – 5 – 17 is NOT the same as 17 – 31 – 5

PermutationsAn arrangement or listing in which order or placement is important is called apermutation.

Simple example: “combination lock”

31 – 5 – 17 is NOT the same as 17 – 31 – 5

Though the same numbers are used, the order in whichthey are turned to, would mean the difference in the lock

opening or not.

Thus, the order is very important.

The Gamma Zeta Beta fraternity is electing a President, Vice President, Secretary, and Kegger Chair. If the fraternity has 10 members, in how many different ways can the officers be chosen?

Position

President

Vice president

Secretary

Kegger chair

Permutations

person

A

B

C

D

Person

B

C

A

D

Select 4 person as well as their position. So, this is permutation

PermutationThe number of permutations of n objects taken r at a time is the quotient ofn! and (n – r)!

! !rn

nPrn

Permutations

Use the formula 10 person for 4 position

10 !(10 − 4 ) !

10 !6 !

10∗9∗8∗7∗6 !6 ! 5040

Formula for permutation without repetition

Formula for permutation with repetition

Permutations

Which is easier to write down using an exponent of r: n × n × ... (r times) =

Use the formula 10 person for 4 position with allow repetition

𝟏𝟎𝟒 10*10*10*10 10000 ways

Solve this without formula

Without repetition

With repetition

Just multiply the remaining person/items for each position

Vice . Ppresident secretary chair

10 789

Vice . Ppresident secretary chair

10 101010

5040

10000

CombinationsAn arrangement or listing in which order is not important is called a combination.

"My fruit salad is a combination of apples, grapes and bananas" We don't care what order the fruits are in, they could also be "bananas, grapes and apples" or "grapes, apples and bananas", its the same fruit salad. It’s combination

CombinationThe number of combinations of n objects taken r at a time is the quotient of n! and (n – r)! * r!

! ! !

rrnnCrn

An arrangement or listing in which order is not important is called a combination.

Combinations

"My fruit salad is a combination of apples, grapes and bananas" We don't care what order the fruits are in, they could also be "bananas, grapes and apples" or "grapes, apples and bananas", its the same fruit salad. It’s combination

CombinationsThe Gamma Zeta Beta fraternity must choose a committee of four members to plan its annual Children’s Hospital fund raiser and beer bash. If the fraternity has 10 members, how many different committees can be chosen?

The order in which the students are chosen does not matter, so this situationrepresents a combination of 10 people taken 4 at a time.

401 CCrn

CombinationsThe Gamma Zeta Beta fraternity must choose a committee of four members to plan its annual Children’s Hospital fund raiser and beer bash. If the fraternity has 10 members, how many different committees can be chosen?

The order in which the students are chosen does not matter, so this situationrepresents a combination of 10 people taken 4 at a time.

1*2*3*4!6!6*7*8*9*10

! 4 )!410(!10 410

C

210or 24

5040

There are 35 different groups of students that could be selected.

Combination without repetition

𝒏!𝒓 ! (𝒏−𝒓 ) !

Combination with repetition

(𝒓+𝒏−𝟏 )!𝒓 ! (𝒏−𝒓 ) !

Where n is the number of things to choose from, and we choose r of them

Number of remaining person/item divided by position then multiply each slot

10❑ ∗ 9

❑∗ 8❑∗ 7

❑

Combination without repetition

Combination without formula

101 ∗ 9

2 ∗83 ∗

74

Combination without formula

Combination without repetition

Number of remaining person/item divided by position then multiply each slot

Combination without formula

101 ∗ 9

2 ∗83 ∗

74

504024 210

Combination without repetition

Number of remaining person/item divided by position then multiply each slot

When working with permutations and combinations, it is vital that youare able to distinguish when the counting order is important, or not.

This is only recognizable after a considerable amount of practice.

Combinations

When working with permutations and combinations, it is vital that youare able to distinguish when the counting order is important, or not.

This is only recognizable after a considerable amount of practice.

When the order doesn't matter, it is a Combination. dot When the order does matter it is a Permutation.

Combinations

When working with permutations and combinations, it is vital that youare able to distinguish when the counting order is important, or not.

This is only recognizable after a considerable amount of practice.

When the order doesn't matter, it is a Combination. dot When the order does matter it is a Permutation.

"My fruit salad is a combination of apples, grapes and bananas" We don't care what order the fruits are in, they could also be "bananas, grapes and apples" or "grapes, apples and bananas", its the same fruit salad. It’s combination

Combinations

When working with permutations and combinations, it is vital that youare able to distinguish when the counting order is important, or not.

This is only recognizable after a considerable amount of practice.

When the order doesn't matter, it is a Combination. dot When the order does matter it is a Permutation.

Combinations

"The combination to the safe is 472". Now we do care about the order. "724" won't work, nor will "247". It has to be exactly 4-7-2. it’s permutation

"My fruit salad is a combination of apples, grapes and bananas" We don't care what order the fruits are in, they could also be "bananas, grapes and apples" or "grapes, apples and bananas", its the same fruit salad. It’s combination

A Permutation is an ordered Combination. thought To help you to remember, think "Permutation ... Position"

Thank you