Asked by Tom
A committee of 5 people is to be selected from student council. Council has 6 boys and 7 girls. What is the probability that the committee will have at least 3 boys?
*** If you can show work that would be helpful (OPTIONAL)***
THANK YOU VERY MUCH!
*** If you can show work that would be helpful (OPTIONAL)***
THANK YOU VERY MUCH!
Answers
Answered by
MathMate
Define
C(n,r)=n!/(r!(n-r)!)=n choose r
Sample space: C(13,5)=1287
ways to choose 0 boy
=Choose 5 girls out of 7 and 0 boy out of 6
=C(7,5)*C(6,0)=21
ways to choose 1 boy:
=C(7,4)*C(6,1)=210
ways to choose 2 boys:
=C(7,3)*C(6,2)=525
ways to choose 3 boys:
=C(7,2)*C(6,3)=420
ways to choose 4 boys:
=C(7,1)*C(6,4)=105
ways to choose 5 boys:
=C(7,0)*C(6,5)=6
If you add them all up, they will total 1287 as required.
Now make appropriate sums according to requirements and calculate probability.
C(n,r)=n!/(r!(n-r)!)=n choose r
Sample space: C(13,5)=1287
ways to choose 0 boy
=Choose 5 girls out of 7 and 0 boy out of 6
=C(7,5)*C(6,0)=21
ways to choose 1 boy:
=C(7,4)*C(6,1)=210
ways to choose 2 boys:
=C(7,3)*C(6,2)=525
ways to choose 3 boys:
=C(7,2)*C(6,3)=420
ways to choose 4 boys:
=C(7,1)*C(6,4)=105
ways to choose 5 boys:
=C(7,0)*C(6,5)=6
If you add them all up, they will total 1287 as required.
Now make appropriate sums according to requirements and calculate probability.
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