SAT question?

Question

In a certain flower shop, only 3 vases of flowers and 1 wreth can be displayed om the front of the window at one time. If there are 10 vases of flowers and 4 wreaths to choose from, how many different arrangements of vases and wreaths are possilbe?

THANKS

Answer 1

You multiply all possible options.

10 * 9 * 8 * 4 = 2880

It goes 10 9 8 for vases because after you pick one out of 10, you have 9 left, then 8, etc... And you only choose one wreath so you just multiply by 4.

Answer 2

This is a combinatorics question. The answer is:

( 10) = (10*9*8*7*6*5*4*3*2*1)/ (3*2*1)*(7*6*5*4*3*2*1)
( 3)
= 120 Vase arrangements


( 4) = (4*3*2*1)/(3*2*1) = 4 Wreath Arrangements
( 1)

4 Wreath Arrangements * 120 Vase arrangements =
480 possible arrangements

Answer 3

3 out of 10 vases:
10*9*8=720 if the order matters or 10*9*8/1*2*3=120 if the order doesn't matter.
1 out of 4 wreaths: 4 choices.
if the order doeasnt matter, 120*4=480 possibilities.
if the order matters but the wreath can only be in 1 place:
720*4=2880 possibilities

Answer 4

There are 10C3 = 10*9*8/3! = 120 combinations of vases and 4 wreath combinations. For a total number of cominations of:

4*120 = 480

Answer 5

(the number of combinations of 10 things taken three at a time) multiplied by (the number of combinations of 4 things taken one at a time)

(10! / ( (10-3)! * 3!) ) * ( 4! / ((4-1)! * 1!))

10! / ( 7! * 3! ) * 4

(10*9*8 / 3*2*1 ) * 4

720 / 6 * 4

480


That is if you don't care about the order in which they are displayed. If you care about the order, then it's 10*9*8*4 = 2880.

Answer 6

Order is not important, so we will use combination

10C3 + 4C1 = 124 different arrangements of vases and wreaths