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