Find the probability three balls randomly taken out of the box will be red

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 =
C
310
/C
315
=
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


Answer: probability all three balls are red is
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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Monday, November 23, 2020
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