A student council is to be chosen from a class of 12 students consisti

Question

A student council is to be chosen from a class of 12 students consisting of a president, a vice president, and 3 committee members. How many such councils are possible

(A)  \frac{12!}{7!5!}

(B)  \frac{12!}{7!3!}

(C)  \frac{12!}{3!5!}

(D)  \frac{12!}{7!}

(E)  12!

UB001 · Answer

A student council is to be chosen from a class of 12 students consisting of a president, a vice president, and 3 committee members. How many such councils are possible

Choosing 5 members from 12 = 12C5 = 12!/ (7! 5!)
 Answer Option A is Correct.

nmccull · Answer

Wouldn't this need to be a permutation because of the different positions? That would be 12!/7!, but adjust for 3 positions being the same 12!/(7!3!). I'm not certain, but that is my initial thought.

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kanakdaga · Answer

I think so too. 
a permutation problem is one that is dependent on arrangement. That means : (a,b) is not equal to (b,a).
A combinations problem is one where (a,b) = (b,a).
Here, we are choosing 5 people out of 12. 
But a person chosen for president will be a separate combination than to the person chosen as vice president. Thus, arrangement matters.
so its a permutations problem. thus 12P5

nmccull · Answer

"I think so too. 
a permutation problem is one that is dependent on arrangement. That means : (a,b) is not equal to (b,a).
A combinations problem is one where (a,b) = (b,a).
Here, we are choosing 5 people out of 12. 
But a person chosen for president will be a separate combination than to the person chosen as vice president. Thus, arrangement matters.
so its a permutations problem. thus 12P5"

Yes I am pretty confident it is a permutation, but does it need to be adjusted for the fact that there are only 3 unique positions? 12p5 implies 5 unique positions for arrangement, but there are only 3 in this case (president, vice president, and council member).

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kanakdaga · Answer

You mean that choosing the council members would be a combination while for the three positions it is a permutation ? 
 lets consider people : a , b, c ,d, e

a as president = 1 way

a as vice president = 1way

a,b,c as council members = 1 way
but a,b,c = b, c, a = c, a, b

thus 3 positions as permutation ?

nmccull · Answer

Yes, that is how I interpreted the scenario.

kanakdaga · Answer

check this question out. https://gmatclub.com/forum/a-club-has-1 ... fl=similar your reasoning sounds correct though.

eswarchethu135 · Answer

A president can be chosen in 12 ways. Vice president in 11 ways. Remaining 3 committee members can be selected in  10_C_3  ways =  \frac{10!}{7!3!}

So total possible ways are  \frac{12!}{7!3!}

OPTION:  B

Manat · Answer

chetan2u  or  VeritasKarishma  could you please explain how is it a Permutation problem? & the solution

chetan2u · Answer

Hi ..

It is a combination of permutation and combination..

Out of 12 you have to choose a president, vice president and 3 committee members..
So choosing president and vice president is permutation and selection of 3 committee members is combination.

Go step by step..
1) president - any of the 12, so 12 ways
2) vice president - any of the remaining 11, so 11 ways
3) 3 committee members - 3 out of 10, so 10C3..

Total ways =  12*11*10C3=12*11*\frac{10!}{7!3!}=\frac{12!}{7!3!}

B

Kinshook · Answer

Given: A student council is to be chosen from a class of 12 students consisting of a president, a vice president, and 3 committee members.

Asked: How many such councils are possible

Number of ways such councils are possible = 12C1*11C1*10C3 = 12*11*10!/3!7! = 12!/7!3!

IMO B

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A student council is to be chosen from a class of 12 students consisti

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