Calculate the probability that among the selected seven people will be three girls

Problem description:
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.

Problem solution:
The number of choices selecting 7 people out of 10 equals is:
C
710
=
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
34
× C
46
=
4!/(4 - 3)! × 3!
×
6!/(6 - 4)! × 4!
= 4 ×
6 × 5/1 × 2
= 60


Therefore, the sought probability is equal to
C
34
× C
46
/C
710
=
60 × 3! × 7!/10!
=
60 × 2 × 3/8 × 9 × 10
=
1/2
= 0.5


Answer: probability of selecting three girls among the seven selected people will be 0.5


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

Unit Calculator ALLin1
Monday, November 23, 2020
Contact
Privacy Policy
Terms & Conditions

Copyright © 2020 Intemodino Group s.r.o.
All rights reserved
Menu