Permutations and Combinations Made easy
Posted on : 19-01-2021 Posted by : Admin

.

Permutation and combination: An Idea

Permutation is arrangement of things in a definite order. Here ORDER IS IMPORTANT.

Combination is selection (choosing) the things. Here ORDER IS NOT IMPORTANT

In our day-to-day life we use this concept of permutations and combinations to know the number of ways a particular work can be done. For example let us consider four persons A, B, C and D. But there is only one President post. And if we want to know that in how many ways this post can be given to one person then,

Case President Not selected
I A B, C, D
II B A, C, D
III C A, B, D
IV D A, B, C

Hence the number of ways this post can be given is four.

Similarly,

For selecting persons to be seated in two given chairs in a row. We have only two persons A and B.

  • Case I, we can select A at first place and B in second place.
  • Case II, we can select B for the first place and A for the second place.

So the only possible ways of arranging A and B in a row is AB and BA. Here please note that we are considering the order of things.

 

Permutation

Permutation is the arrangement of things.In permutation, the order of arrangement of the things is important. So, in other words we can say that permutation is the arrangement of things in a definite order.

Let us permutate two letters from a group of four letters A, B and C.

AB, BA, BC, CB, AC, CA

Uses of Permutations:

  • Forming wordes with given letters
  • Forming numbers with given digits
  • Arranging people in row
  • Arranging people at a round table
  • Arranging books on a book shelf

 

Combination

Combination is the arrangement of things. In Combination, the order of arrangement of the things is NOT important. So, in other words we can say that combination is the selection of things.

Let us say for example, the combination of two letters from th group of three letters A, B and C would be,

AB, BC AC

Here we have made groups. group AB is same as group BA because the order is NOT important.

Uses of Combinations:

  • Forming committee from given set of people
  • Selecting books from a book shelf

Formulae-Permutations and Combinations

  • n! = 1 × 2 × 3 × 4 ×........× (n-1) × n
  • Number of permutations of n different objects taken r at a time is given by,

            Prn=n!(n-r)!=n (n-1) (n-2).... (n-r+1)

  • Number of combinations of n different objects taken r at a time is given by,

            Crn=n!(r!) (n-r)!=n (n-1) (n-2).... rr!

  • Number of permutations of n objects taken all at a time is n!
  • Number of permutations of n different objects taken r at a time when repitition is allowed is nr
  • Number of circular permutations of n objects is (n-1)!
  • In a circular permutation, if clockwise and anticlockwise arrangements are same, then the number of circular permutations of n objects is,

              (n-1)!2

  • Number of permutations of n objects out of which p are of same (first) type, q are of same (second) type and r of same (third) type is given by,

              n!(p!) (q!) (r!)

  • nCn =1
  • nC0 =1
  • nCr = nCn =1
  • nCx = nCy  ⇔ x=y (or) x+y=n

Hope you have liked this post.

Please share it with your friends through below links.

All the very best from Team Studyandscore

“Study well, Score more…”

- Share with your friends! -