A university needs to select a nine-member committee on extr

Question

A university needs to select a nine-member committe on extracurricular life, whose members must belong either to the student government or to the student advisory board. If the student government consists of 10 members , the student advisory board consists of 8 members and 6 students hold membership in both organiztions , how many different committes are possible.

a) 72
b) 110
c) 220
d) 720
e) 1096

A. 72
B. 110
C. 220
D. 720
E. 1096

Bunuel · Accepted Answer

Two groups:
Student government = 10;
Student advisory board = 8;
Both = 6.

Total # of members of either of group is: 10+8-6=12.

# of ways to choose 9 people out of 12 is  C^9_{12}=\frac{12!}{9!3!}=220 .

Answer: C.

Hope it helps.

b2bt · Answer

is the difficulty really sub600?
I find it more difficult.

kinjiGC · Answer

I think it is 600-700 level. Compared to OG which are sub 600, this question is actually good.

Combination of two concepts (Venn Diagram and Combination) -> 600-700 level.

healthjunkie · Answer

How is 9C12 = 220? I keep getting just 20.

kinjiGC · Answer

12C9 = 12 ! /(9! * 3!) = 10 * 11 * 12/ 2*3 = 10* 11 * 2 = 220.

I hope this is clear.

roro555 · Answer

Hello,

Step 1:
student government consists of 10 members + the student advisory board consists of 8 members (so add them): 10 + 8 = 18

Step 2:
6 students hold membership in both organizations ( so subtract from total in step 1): 18- 6 = 12

Step 3:
How many different committee are possible if 9 will be selected.
So 12! / 9! 3! (9 will be selected and 3 will not be selected).

12 x 11 x 10 / 3 x 2 x 1 = 220 Answer is C.

mdeep92 · Answer

Total number of students = 10+8-6 = 12. Ways to select 9 out of 12 = 12C9 = 12*11*10/3*2=220

Sent from my ONE A2003 using Tapatalk

hdwnkr · Answer

No. of students in government = 10
No. of students in advisory board = 8
No. of students in both = 6
Total = 10 + 8 - 6 = 12

Total number of 9 member committees would be 9C3 = 220.

I wonder if the question could be made a 700 difficulty one by adding constraints. Such as exactly one student should be from the one of the two groups. Food for thought!

JeffTargetTestPrep · Answer

The number of students who belong either to the student government or to the student advisory board or both is:

Total = # Government + # Advisory - # Both + # Neither

10 + 8 - 6 + 0 = 12 students.

So the number of ways to select the 9-member committee out of 12 possible candidates is 12C9:

12!/

12!/(3! x 9!) = (12 x 11 x 10)/3! = (12 x 11 x 10)/(3 x 2) = 2 x 11 x 10 = 220

Answer: C

Fighter28 · Answer

Kudos pls, if you like the post

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A university needs to select a nine-member committee on extr

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