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