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.

There are 15 balls in the box, so, the number of choices for three balls:

C^{3}_{15} =

15!/(15 - 3)! × 3!

There are 10 red balls, so the number of choices for three red balls out of ten red is:

C^{3}_{10} =

10!/(10 - 3)! × 3!

Therefore, the probability P that the three selected balls are red, is:

P =

C^{3}_{10}/C^{3}_{15}

= 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

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