in a competition 5 figure skaters will skate in a randomely assigned order. why can't you evaluate the product 5*5*5*5*5 to find the number of possible orders in which the skaters can skate
there are 5 skaters sitting in a penalty box.
A B C D E
You pull one out at random.
Say it is C and our chance is 1/5 for picking C
NOW WE HAVE 4
A B D E
Say it is A and our chance is 1/4 for picking A ( NOT 1/5 !!!!)
Next we pick B (1/3)
Next D (1/2)
Next E (1/1 or 1)
SO
our chances of picking that order are
(1/5)(1/4)(1/3)(1/2)(1/1)
or
1/5!
SO
and the number of possible orders is
5! = 120
To find the number of possible orders in which the skaters can skate, you cannot simply evaluate the product 5*5*5*5*5. This is because the number of possible orders is not determined by multiplying the number of skaters (5) by itself 5 times.
The reason for this is that in a competition, once a skater has performed, they are no longer available to perform again. Therefore, the number of possible orders decreases with each skater who performs.
To find the number of possible orders, you need to use a concept called permutations. In this case, since all 5 skaters will skate in a randomly assigned order, you need to find the number of permutations of 5 objects taken all at once.
The formula to calculate the number of permutations is given by:
n! / (n - r)!
where n is the total number of objects (in this case, skaters) and r is the number of objects you want to arrange (in this case, all 5 skaters).
Using this formula, the number of possible orders in which the skaters can skate can be calculated as:
5! / (5 - 5)! = 5! / 0! = 5! / 1 = 5! = 5 * 4 * 3 * 2 * 1 = 120
Therefore, there are 120 possible orders in which the skaters can skate.