Marla is on the student council. The council will choose 3 members at random to run the drive. There is a 50% chance that Marla will be chosen. How many students are on the council?
+128473 The total number of sets of 3 people that can be selected from P people = C(P, 3)
And the total number of sets of 3 people that can be selected from (P - 1) persons (which will not include Marie) = C(P-1 , 3)
So....we want to solve this
C(P-1, 3)
________ = 1/2
C (P, 3)
C(P - 1, 3) = (1/2) * C(P, 3)
Using the combinations formula, we have that
(P -1)! P!
____________ = (1/2) * ________
(P - 1 - 3)! 3! (P - 3)! 3!
(P - 1)! P!
______ = (1/2) _____
(P - 4)! (P - 3)!
(P - 1)! (P - 3)! 1
____________ = ____
P! (P - 4)! 2
P - 3 1
______ = ____ cross-multiply
P 2
2(P - 3) = P
2P - 6 = P
P = 6 = the number of students on the council
