106oh no nishant sir ...
the (i) (ii) ... are the conditions to be held simultaneously
this was a question of ADG..
so, if subsets are distinct the answer should be 12!(4!)3
The number of ways in which a set A where n(A) = 12 can be partitioned in three subsets P,Q,R each of 4 elements subject to the following conditions
(i) P U Q U R = A
(ii) P ∩ Q = φ
(iii) Q ∩ R = φ
(iv) R ∩ P = φ is
Doubt is should we consider the subsets as identical or different as in distribution of 12 different things in 3 identical boxes or distribution of 12 different things in 3 different boxes
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5 Answers
62The first one will be 712
2nd will be 512
3rd and 4th will be also 512
Subsets should be distinct... (I think) even though that should be explicityly mentioned.
10662oh .. yeah i din read the second part... (all sets contain 12 elements ) :P
ANd yeah here you should consider them as distinct.. because they are named as P, Q, R
If the quesiton was any three subsets then I would have put my bet on identical..
62okie.. dont worry about these ambiguities as long as you are clear with what case will lead the right answer.. bcos iIt will not have a question which is vague