Permutation and combination is one of the fundamental topics in maths that comes with a plethora of applications in modern technology and in its evolution.It is widely used in statistics, probability and in the solution of many real world problems.So lets see how the knowledge of it is plays an instrumental role in our daily life.
.jpg "permutation and combination")
.jpg "permutation and combination")
What is Permutation
Whenever we talk of arrangements we can use permutation there Or when you want to know possible arrangements by putting things in a specific order. It would be easier to understand it with simple examples to complex ones.
Example 1 : How many meaningful or meaningless 2 letter words can be made from the word "Hi"?
Let's count the number of letters:
1. Hi
2. iH
3.HH
4. ii
In this word we allowed repetition of letters so we got 4 words but If it was not allowed we would get 2 words only.
1. Hi
2.iH
Example 2 : How many meaningful or meaningless 3 letter words can be formed from the letters of "PIN"
Let's see the possibile arrangements:
1.PIN
2.INP
3.NPI
4.PNI
5.NIP
6.IPN
7.PPP
8.NNN
9.III
Total number of words= 9
Without Repetition the total number of words= 6
Example 3: A digital lock opens with a three digit number.but the owner of the lock forgot third digit and the starting two digits are 4 and 2.Now let's see how many password he can try to open this lock?
Ans : Since two digits are known so we have to ascertain the last digit only.Hence the number of Permutations
4,2,0
4,2,1
4,2,2
4,2,3
4,2,4
4,2,5
4,2,6
4,2,7
4,2,8
4,2,9
So as you can see there is a total of 9 permutations exist.
Or we can simply say,the last digit could be any number from 0 to 9 Hence there are 9 possible passwords to open the lock.
What is combination
When the order of things things is not important while grouping them we are generally using combination.
Example 1 : Carry,Adam and Neo three friends want to form a group of two friends.how many such groups can be formed?
However permutation can be used but we can't use permutation to get correct result.we will first use permutation then combination.
Let's see the total number of permutation
1. Carry, Adam
2. Adam,Carry
3. Neo, Adam
4. Adam,Neo
5. Carry,Neo
6.Neo, Carry
Using permutation the number of groups= 6.
But practically only 3 groups are possible.
Why three groups?
Let's understand.
Carry,Adam or Adam, carry are not different groups they both points to the same group.as we have discussed earlier,In combination order doesn't matter.
Similarly, The rest of 4 group give 2 unique groups.
Total number of unique groups = 3 groups.
Example 2 : Five friends gather for a function and they all shake hand with each other.What are the number of handshakes ?
Ans : There are five friends so 5 hands are used for shaking.For one handshake at least two hands are required.