A photographer is takinh pictures for the school yearbook. She positions the 9 members of the chess club in one row. How many ways can the photographer

Question

arrange the members of the chess club in a row?

Answer 1

Janice,

 

This is a factorial problem, and the answer is 9!.  

 

If that is hard to understand, think of it this way.  There are nine positions in the row, right?  That means that for the first position there are 9 possibilities.  After the photographer puts someone there--it doesn't matter which one--there are only 8 possibilities for position two, because somebody has to be in position one.  For the third position, there are 7 possibilities, for the fourth, 6, etc.  No matter who is in any particular position, there will be limitations on who is available to come next.

 

These events are related, so we multiply the possibilities for each position: 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1.  The answer is 362,880.  That's a lot!  

 

But not too many to be plausible.  Imagine there were only two people in the line:  the answer would obviously be 2 possibilities, right?  That equals 2!, or 2 x 1.  What about three?  Well, that would be 6 possibilities; it's a little less obvious, but you can assign the people letters, a,b, and c, and see it:

 

a,b,c

a,c,b

b,a,c

b,c,a

c,a,b

c,b,a

 

And 6 possibilities is 3!, or 3 x 2 x 1.  

 

If this system works for two and three people, there is no mathematical reason why it wouldn't work for 4, 5, 9... or 9,000!  The number of possibilities gets big, fast.

 

Hope this helps,

 

Evan