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greatest number of distinct teams

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by LalaB » Thu Sep 29, 2011 4:18 am
A Â…firm is divided into four departments, each of which contains four people. If a project is to be assigned to a team of three people, none of which can be from the same department, what is the greatest number of distinct teams to which the project could be assigned?

(A) 4^3
(B) 4^4
(C) 4^5
(D) 6(4^4)
(E) 4(3^6)

B
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Source: — Problem Solving |

by shankar.ashwin » Thu Sep 29, 2011 4:46 am
First selecting 3 teams from 4 can be done in 4C3 ways = 4

After selecting the 3 teams, I can select any of the 4 members in each team; 4 * 4 * 4

In total, 4*4*4*4 = 4^4 ways
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