SOLUTION: There are ten boys and twelve girls in the Leadership class. The homecoming committee has 4 members that will be picked from the lead class. What is the probability that the homeco
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Question 311193: There are ten boys and twelve girls in the Leadership class. The homecoming committee has 4 members that will be picked from the lead class. What is the probability that the homecoming committee will have at least three girls?
You can put this solution on YOUR website! There are ten boys and twelve girls in the Leadership class. The homecoming committee has 4 members that will be picked from the lead class. What is the probability that the homecoming committee will have at least three girls?
To have a successful committee we must have
3 girls AND 1 boy OR all 4 girls
The number of ways to choose 3 girls and 1 boy:
We can choose the 3 girls 12C3 ways AND the 1 boy 10C1 ways.
AND means multiply so we have (12C3)(10C1)=(220)(10)=2200 ways to choose 3 girls and 1 boy.
We can choose 4 girls and 0 boys (12C4)(10C0)=495 ways.
That's a total of 2200+495 or 2695 to successfully have 3 or 4 girls.
The total number of ways to pick any 4 from the total 22 in the lead class
is 22C4 or 7315.
Therefore the probability of at least 3 girls is
That reduces by dividing numerator and denominator by 385 to
(which is about a 37% chance).
Edwin
