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Let me know how much time you took .. - thanks.. A teacher [#permalink]

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28 Jun 2006, 02:51

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Let me know how much time you took .. - thanks..

A teacher is assigning 6 students to one of three tasks. She will assign students in teams of at least one student and all students will be assigned to teams. If each task will have exactly one team assigned to it, then which of the following are possible combinations of teams to tasks?

I. 90
II. 60
III. 45

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III

Not able to understand it, Please can someone explain how we got 60,90, and 30 values.

The first combination is 1, 2 , 3

One person in a team can be chosen in 6C1
2 persons from 5 left = 5C2
3 persons from 3 left = 3C3
Hence = 6C1*5C2*3C3 = 60

The second combination is 2, 2, 2
2 persons from 6 can be chosen in 6C2
2 persons from 4 can be chosen in 4C2
2 persons from 2 can be chosen in 2C2
Hence 6C2*4C2*2c2 = 90

The third combination is 4,1,1
4 persons from 6 can be chosen in 6C4
1 person from 2 can be chosen in 2C1
1 person from 1 can be chosen in 1C1
Hence 6C4*2C1*1C1 = 30

Not able to understand it, Please can someone explain how we got 60,90, and 30 values.

The first combination is 1, 2 , 3

One person in a team can be chosen in 6C1 2 persons from 5 left = 5C2 3 persons from 3 left = 3C3 Hence = 6C1*5C2*3C3 = 60

The second combination is 2, 2, 2 2 persons from 6 can be chosen in 6C2 2 persons from 4 can be chosen in 4C2 2 persons from 2 can be chosen in 2C2 Hence 6C2*4C2*2c2 = 90

The third combination is 4,1,1 4 persons from 6 can be chosen in 6C4 1 person from 2 can be chosen in 2C1 1 person from 1 can be chosen in 1C1 Hence 6C4*2C1*1C1 = 30