SOLUTION: Mrs. Hernandez wants to put a picture of each of her 3 children on a shelf above her desk. In how many ways can she line up the pictures?

Question 503945: Mrs. Hernandez wants to put a picture of each of her 3 children on a shelf above her desk. In how many ways can she line up the pictures?
Found 2 solutions by josmiceli, oberobic:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Call the pictures , , and
The orderings are:
a b c
b c a
c a b
b a c
a c b
c b a
there are 6 different ways to arrange he pictures
the way to calculate it is:
(3 possible in 1st position)x(2 left in 2nd position)x( 1 left for last position) = 6 different ways
You would need to calculate this way if there
were 10 children:
possible orders
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
She has 3 choices for the first position.
But once she makes her choice, she only has 2 choices for the second position.
And once she makes her second choice, she has on 1 choice for the third position.
3*2*1 = 6
There are 6 ways she can line up the pictures.
As it so happens, this is the definition of 3! (3 factorial).
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