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# help

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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?

Dec 17, 2019

#1
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x memebers on the council:

50% * x = 3

x =3 / 50% =6 students on the council.

Dec 17, 2019
#2
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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   Dec 17, 2019