There are six boys and four girls in the group.

Seven people are randomly selected from the group.

What is the probability that among the selected seven people will be three girls.

The number of choices selecting 7 people out of 10 equals is:

C^{7}_{10} =

10!/(10 - 7)! × 7!

If there are 3 girls among 7 people, then the remaining 4 people are boys.

The number of choices of 3 girls and 4 boys is equal to:

C^{3}_{4} × C^{4}_{6} =

4!/(4 - 3)! × 3!

× 6!/(6 - 4)! × 4!

= 4 × 6 × 5/1 × 2

= 60Therefore, the sought probability is equal to

C^{3}_{4} × C^{4}_{6}/C^{7}_{10}

= 60 × 3! × 7!/10!

= 60 × 2 × 3/8 × 9 × 10

= 1/2

= 0.5Next probability problem solution: Calculate the chance of getting six on at least one dice of three dice

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