## Combinations When Order of Precedence is Not Taken Into Account

We have to pick from a selection of objects, and need to know, in how many ways canobjects be picked from a choice of

There are complications. If the is no order of preference, then the order of the selection does not matter. If you are choosing which library books to take out, then the order in which you choose the books will not matter. What will matter will be the selection you make, whatever the order you make it in. If you want to take out 5 books on statistics from your local library, which has 100 books on statistics available.

You may pick your first choice from one of 100.

You may pick your second choice from one of 99.

You may pick your third choice from one of 98.

You may pick your fourth choice from one of 97.

You may pick your fifth choice from one of 96.

Hence there are 100*99*98*97*96 possible ways of picking five statistics books from 100, without regard to preference.

The same consideration would apply when considering the number of ways in which passengers get into a bus, if there are more passengers than seats. Obviously it will be the selection of passengers that get on the bus, not the order. contestants can occupy the first three places in a races, since the order obviously matters. In general the number of ways in which a choice ofobjects can be picked fromobjects is

Suppose that we have to pick from several groups and we want to find the total number of possible choices. A manager of a national football team could be choosing his team to take to the World cup. He has to choose a goalkeeper, defenders, midfielders and strikers. He is allowed to take 23 players, of which 3 must be goalkeepers. If all players of of the same quality, he will have no order without respect to preference. He chooses to take 6 defenders, 8 midfielders and 8 strikers.

Suppose he can pick from 10 possible goalkeepers. Then he can pick inways without respect to precedence.

Suppose he can pick from 13 possible defenders. Then he can pick inways without respect to precedence.

Suppose he can pick from 11 possible midfielders. Then he can pick inways without respect to precedence.

Suppose he can pick from 15 possible goalkeepers. Then he can pick inways without respect to precedence.

Hence he can choose his squad inways altogether.