0Q: There are 9 objects and 9 boxes. Out of nine objects, 5 can not fit in three small boxes. How many arrangements can vere made such that each object can put in one box only?
Ans : As 5 objects can not fit in 3 boxes, these 5 objects can be placed in other 6 boxes. 5 objects can be placed in 6 boxes in 6P5 ways. The remaining 4 objects can be placed in remaining 4 boxes in 4! ways.
Therefore required numbers of arrangements = 6P5 × 4!
= 720 × 24 = 17280.
