Question

In how many ways can $6$ distinguishable objects be distributed in four distinguishable boxes such that there is no empty box?

Answer 1

Pick and arrange 4 objects such that each object goes into one box $:{}^4{P}_3$

Place the other two objects into any of 4 boxes $:4\times 4$

$\therefore$ total number of ways $={}^4{P}_3\times 16=2880$