Permutation & Combination
PNC
Introduction of selection/combination:-
Let us assume that Suresh has 5 friends A, B, C, D, E and he want to invite 2 of them for a party.
So the question is how many ways he can invite 2 friends out of 5 friends.
First Let us do it manually ⇒
A B C D E
Number of ways ⇒
(A, B) (A, C) (A, D) (A, E)
(B, C) (B, D) (B, E)
(C, D) (C, E)
(D,E)
= 10 ways
Since here we are to select 2 out of 5 values which we can do manually but if these numbers ↑ then it will become difficult to do it manually. So we will do it with the help of a formula.
⦿ Number of ways of selecting ‘r’ articles from ‘n’ distinct article is :-
Example:- Suresh has a party at his home. He has 12 friends & want to invite only 3 of them. In how many ways he can do this?
Solution:-
= 220 ways Answer
⦿ Number of ways of selecting ‘r’ articles from ‘n’ distinct articles if ‘k’ article is always included :-
Example:- In how many ways kapil can call 5 of his 12 friends if amit & ankit are always included?
Solution:-
¹²⁻²C₅₋₂
= ¹⁰C₃
= 120 Answer