There are 10 boys and 13 girls in Mr. Benson\'s fourth- grade class. A picnic co

Question

There are 10 boys and 13 girls in Mr. Benson's fourth- grade class. A picnic committee of five students is selected at random from the students in the class. How many ways are there to select a committee with only boys? How many ways are there to select a committee with five students? What is the probability that all the committee members are boys? What is the probability that the committee has three girls and two boys? What is the probability that the committee has at most 3 boys in the committee?

Explanation / Answer

a) There are 10 boys and need to select 5, without replacement and order does not matter.
Therefore, 10C5 = 10!/(5!*5!) = 252 ways

b) There are 23 students in total and need to choose 5
23C5 = 33649

c) P(all selected are boys) = 10C5/23C5 = 36/4807 = 0.0075

d) P(3 girls and 2 boys) = (10C2 * 13C3)/23C5 = 0.3825

e) P(at most 3 boys) = 1 - P(4 boys) - P(5 boys) = 1 - (10C4 * 13C1)/23C5 - (10C5 * 13C0)/23C5 = 0.9114

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.