Math formula?help????

Question

Allen has a cat a golfish and a dog.He ffeds them in a different order every day. How many different ways can he feed his pets?

Isn't there a formula for figuring this out?

Answer 1

cant remember the formula but 6 ways:

cdg

cgd

dcg

dgc

gcd

gdc

Answer 2

yes, there is:

the # of ways to order n number of things is 1 x 2 x 3 ... x n = n!

in this case there are 6 ways to order the three feedings

to see why the formula is true:

there is obviously 1 way to order one thing

example cat

for two things: the second thing can be before or after the first thing

example cat dog, or dog cat

now for each of those two, goldfish can go before both, after both, or in the middle, so the 3 x 2 total possibilities = 6

and for each of those 6, there possibilities, there would be 4 ways to add, say, a giraffe to the feeding order, and so on

Answer 3

order doesn't matter

so you use permutation

3 diff objects/things/animals, so you do

3! = 3*2*1 = 6 different combinations possible.

Permutation notation is

X!

which means X * X-1 * X-2 * X-3 * .... * 1

where X = number of objects, and in your case, 3 is the number of objects.