discrete mathematics self doubt

Question

how we come to know that whether in question we apply combination or permutation ..??

how can i make difference b/w both ?

Answer 1

This is one of the fundamental yet confusing doubts one has in this very topic..

I will try to let u understand through a simple example..

Problem :   How many ways can we select a cricket team of 11 players out of a squad of 13 players.

Now here say we have selected a team of 11 players..Hence we are concerned about selection of players only but not arrangement among them..Hence this becomes the problem of combination.

Here no of ways   =    ¹³C₁₁ only.

Now lets modify the above problem to make it a permutation problem..

Problem :   How many batting orders can be made from a cricket team of 11 players out of a squad of 13 players.

Now here arrangement among the selcted players matter..[ Say Virat Kohli batting at no 4 instead of no 3 , so it will be considered as different only..:) ]

Here no of ways hence    =  Selection of 11 players from 13 player squad * Batting orders possible among the selected 11players 

                                     =  ¹³C₁₁  *  11!

                                     =  ¹³P₁₁

Hope this helps..:)

Comments

thanks sir got it..!
 

 

COMBINATION- *selection and  unorder

PERMUTATION- * arrangement and order matter