Problem description:
There are fifteen balls in the box: ten red balls and five white ones.
Three balls are randomly taken out of the box.
Find the probability all three balls are red.
Problem solution:
There are 15 balls in the box, so, the number of choices for three balls:
C
315
=
15!/(15 - 3)! × 3!
There are 10 red balls, so the number of choices for three red balls out of ten red is:
C
310
=
10!/(10 - 3)! × 3!
Therefore, the probability P that the three selected balls are red, is:
P =
=
10! × (15 - 3)! × 3!/(10 - 3)! × 3! × 15!
=
10! × 12!/7! × 15!
=
8 × 9 × 10/13 × 14 × 15
=
4 × 3 × 2/13 × 7
=
24/91
24/91
Next probability problem solution:
Calculate the probability that among the selected seven people from the group will be three girls
