Five balls are to be placed in three boxes in how many diff. ways can be placed the balls so that no box remains empty if
(i) balls and boxes are diff,
(ii) balls identical and boxes diff.
(iii) balls diff. and boxes identical
(iv) balls as well as boxes are identical
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i) 150, (ii) 6, (iii) 25, (iv) 2
Sol. Let Boxes contain balls 2, 2, 1 or 3, 1, 1
(i) 
× 3! + 
= 150
(2, 2, 1) (1, 1, 3)
(ii) 1 × 
+ 1 × 
= 6
(2, 2, 1) (1, 1, 3)
(iii) 
× 1 + 
× 1 = 25
(iv) (2, 2, 1) + (1, 1, 3) = 2 ways
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