15 gymnasts are competing in a national competition and will be ranked from 1 to 5
top five gymnasts will then move on to the world competition how many different
ways can the top five gymnasts be ranked?
Order matters in this problem because of the rankings #1 through #5.
There are 15 ways to choose gymnast #1.
For each of those 15 ways to choose gymnast #1, there remain 14 ways
to choose gymnast #2.
That's 15*14 ways to choose gymnasts #1 and #2.
For each of those 15*14 ways to choose gymnasts #1 and #2, there remain
13 ways to choose gymnast #3.
That's 15*14*13 ways to choose gymnasts #1,#2, and #3.
For each of those 15*14*13 ways to choose gymnasts #1,#2, and #3, there
remain 12 ways to choose gymnast #4.
That's 15*14*13*12 ways to choose gymnasts #1,#2,#3 and #4.
For each of those 15*14*13*12 ways to choose gymnasts #1,#2,#3 and #4,
there remain 11 ways to choose gymnast #5.
That's 15*14*13*12*11 ways to choose gymnasts #1,#2,#3,#4 and #5.
So the answer is 15*14*13*12*11 = 360360.
That is sometimes called "15 Position 5" or "15P5" or "P(15,5)" or
"The number of permutations of 15 things taken 5 at a time.
The general formula for the number of n things taken r at a time
is .
So
Edwin