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