The management of a company reviews the performance of 15 employees

15C9 doesn't seem like the correct answer, it doesn't account for the variation of G,S,B coins in selection. In that sense for statement I, 15C13 is also the correct answer.

15C9 just selects 9 ppl to who get the coin. There still can be a variation of how G,S,B will be split amount these 9 ppl = 15C9 x 9C2 X 7C3 X 4C4

Can someone please suggest if my approach is right/ wrong?

I don't understand why the answer is not A. With A, 13 out of 15 employees can receive a coin, so the number of ways to choose 13 employees out of 15 is 15C13. Since each employee is eligible for 1 of the 3 coins, within each 13-employee arrangement, there are 13^3 ways to award a coin to each. Therefore the total number of ways to award 15C13 arrangements of 13 employees is 15C13 * 13^3. Indeed it is a very large number, however, just because the solution is large does not preclude it from being sufficient to answer the question.

I agree with ryangcii2. It's not necessary for us to know how many coins were actually distributed, selection B only gives us a more specific calculation based on the fact that we know this information.

The minimum information needed to know "In how many ways can the company give the coins to the employees" would be
1) how many employees are eligible for coins (we could assume all in the worst case, but we don't)
2) how many coins 1 employee is allowed (if we assume infinity, problem does not make sense since answer is infiniti)
3) how many options of coins do we have (given), how many employees exist (given)

Aabhash777 can you clarify on the OA?

Bunuel your thoughts would be helpful

Statement 1

This statement tells us that total 13 coins are distributed but does not tell us how many of them were gold, silver, and bronze.
And why would we need that information is because :

Instead of 13 coins think that we are talking about Mississippi - s being the gold coins, i being the silver coins and p being the bronze coins.
We need to know how many times they are occurring so that we can factor in the possibilities.

Similarly, we need to know how many gold, silver, and bronze coins were distributed.
Therefore Not Sufficient.

Statement 2

It gives us the relationship of how many coins were distrubted.
2G = 3S = 4B

Now, G, S, and B have to be integer values.
For that to happen, S has to be a multiple of 4 otherwise we won't get integer values for G and B

Say, S=4
G=6, B=3, and S=4 : Total 13 coins

Say, S=8
G=12, B=6, and S=8 : Total 26 coins

Now each student gets only one coin so maximum we can have 15 coins which is satisfied by the first equation.
So we already know the count of the coins.

Sufficient.

If we want we can calculate the number of possibilities of distributing the coins to 15 employees.
First, select 13 employees from 15 employees and then distribute the coins.

\(15C3 * [13! / ( (4!) (6!) (3!) ) ]\)

Hope this helps.

We have 15 employees and for each, 4 options (G, S, B or none[X]). I like to imagine it with a set of blanks that I have to fill

15 employees -> _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

1) 13 coins are given -> we know that two will receive none. _ _ _ _ _ _ _ _ _ _ _ _ _ X X but we do not know who will receive none or if the others will receive only G or only S or only B or a combination, thus not sufficient.

2) G:S:B = 2:3:4 -> Since since they give coins to "some" of them, it cannot be that they will not give any coin. Thus with the ratio given, the total number of coins will be a multiple of 9.

we can only have 9 coins given as 18 is too much (only 15 employees and they cannot receive more than 1). Then we know that our possible array to arrange is

G G S S S B B B B X X X X X X which will be 15!/(2! 3! 4! 6!) -> Sufficient

IMO B

This is a wrong explaination.