Morgan Goldman has 3 Senior Managing Directors and 5 Managing Director

Question

Morgan Goldman has 3 Senior Managing Directors and 5 Managing Directors. Each investment banking deal requires the guidance of three managing directors, at least one of which must be a Senior Managing Director. How many possible investment banking deals can Morgan Goldman possibly provide guidance for?

(A) 16
(B) 36
(C) 46
(D) 54
(E) 64

(A) 16
(B) 36
(C) 46
(D) 54
(E) 64

austinlm · Accepted Answer

Explanation:

There are three different combinations of teams: 3 Senior/0 Manager, 2 Senior/1 Manager, 1 Senior/2 Manager.

3 Senior/0 Manager - Only one possible combination

2 Senior/1 Manager - 3C2 = 3 Senior combinations, 5C1 = 5 Manager combinations ---> 3x5 = 15

1 Senior/2 Manager - 3C1 =3 Senior combinations, 5C2 = 10 Manager combinations ---> 3x10 = 30

1+15+30 =  46

nahid78 · Answer

P(at least 1 S D) = P(Total) - P(0 Senior Director)

=8C3 - 5C3

= 46

mm25 · Answer

Hi how does one go about this Question? I can't seem to understand what it means? Would appreciate your explanation. Thanks!

Bunuel · Answer

Here is the best solution possible for this problem: morgan-goldman-has-3-senior-managing-directors-and-5-managing-director-219210.html#p1689846 Can you please tell me what is unclear there? Thank you.

mm25 · Answer

I don't know why I though that all senior managing directors were also managing directors, i.e., one is a subset of the other? Perhaps I was just over thinking. Anyways, I understand the solution now. Thank you.

flippedeclipse · Answer

The word "at least" signals that we should use the complement method. There's no mention of order, so we can assume it to be a combinations problem.

To use the complement, we find the total number of combinations if there were no restrictions, then subtract the opposite case of what we're looking for - in this situation, the opposite would be if the entire team were made up of managing directors only.

Total combinations:  8C3=\frac{8*7*6}{3*2}=56

Managing Directors only:  5C3=\frac{5*4*3}{3*2}=10

56-10=46

Thus answer is C.

Morgan Goldman has 3 Senior Managing Directors and 5 Managing Director

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Morgan Goldman has 3 Senior Managing Directors and 5 Managing Director

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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