Have two hats. in one hat are balls numbered 1 through 15. in the other hat are balls numbered 16 through 25. i first choose a hat, then from that hat, i choose 3 balls, without replacing the balls between selections. how many different orders selections of 3 balls are possible?

3450 ways

Step-by-step explanation:

Different ways of picking 3 balls from the 1st hat:

1st ball: 15 choices (because there are 15 balls)

2nd ball: 14 choices (because one ball is taken away)

3rd ball: 13 choices (because two ball is taken away)

15*14*13=2730 different possible orders of picking 3 balls from the 1st hat

Different ways of picking 3 balls from the 2nd hat:

1st ball: 10 possibilities (because there are 10 balls)

2nd ball: 9 possibilities

3rd ball: 8 possibilities

10*9*8=720 different possible orders of picking 3 balls from the 2nd hat

720+2730=3450

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional