If we have to select 80 students from a group from 500 students, then this manual approach will be nightmare, thus come Combination to rescue. It gives us a formula to find number of selections easily.
Number of ways of selecting r object from a group of n object is given by n C r = n! /( r! *( n-r)!) Other combination examples
o Ten persons meet in a room and each shakes hand with all the others. How do we determine the number of handshakes? Here, order is not important.
o Six points lie on a circle. How many chords can be drawn by joining these points pair wise?
Permutation means arrangement of things. Order of things is important. Eg; Number of ways in which 3 vacant distinct chairs to be occupied by 5 people.
Combination means selection of things. Order of things has no importance. Eg; Select 3 people from a pool of 5 people
Theorem 5: n Pr = n Cr * r! Where, 0 < r ≤ n We can also say that n Cr = n! / r!( n-r)! Useful Formula
o
o n Cr + n Cr-1 = n + 1 Cr
n
P r = n Cr * r! Where, 0 < r ≤ n. o n! = n *( n-1)!
Numerical: If n C9 = n C8,
Find n C16