Topic 7: Permutations and Combinations With Exercises

√What is Permutations and Combinations?

In mathematics language it will be;

Permutations means when the order does matter however in combination means the order isn't matter. 

Permutations (In other way, A permutation is an ordered Combination)

2 TYPES of permutations:

1) Repetition is allowed example "222"

2) No Repetition for example the first three people in a running race that can't be in first or second.


1) Permutations with Repetition (the easiest to calculate)

When a thing has n in different types ... we have n choices each time!

Example 1: choosing 4 of those things, the permutations are:

n x n x n

(n multiplied 4 times)

In generally, choosing r of something that has n different types, the permutations are:

n x n x .... (r times)

Which in the other words, there are n possibilities for the first choice, THEN there are n possibilities for the second choice, and so on, multiplying each time

Which the exponent is easier to write down using r:

n x n x .. (r times) = nr

Example 2: in the lock above, there are 10 numbers to choose from (0,1,2,3,4,5,6,7,8,9) and we choose 3 of them:

10 x 10 x ... (3 times) = 103 = 1, 000 permutations

Formula:

nr

where n is the number of things to choose from, and we choose r of them (Repetition allowed, order matters)

2. Permutations without repetition

In this case, we have to reduce the number of available choices each time.

Example,

Example 1:

Here is the sample video for permutation:

Here is the sample video of combination:

-EXERCISE-

!GOOD LUCK!

Question 1:

 How many permutations of 3 different digits are there, chosen from the tens digits 0 to 9 inclusive? (Such as drawing en numbered marbles from a bag, without replacement)

a) 84

b) 120

c) 504

d) 702

Question 2:

How many permutations of 4 different letters are there, chose from the twenty six letters of the alphabet?

a) 14 950

b) 23 751

c) 358 800

d) 456 976

Question 3:

In how many ways can the letters of the word 'LEADER' can be arranged?

a) 72

b) 144

c) 360

d) 720