Doubt

Question

can someone explain the formula n^k when k distinguishable items are to be placed in n distinguishable boxes without any restrictions?

Comments

it is equivalent to finding number of functions from set A containing k elements to set B containing n elements.... which is n^k

---

If you have 5 items i1,i2,i3,i4,i5 and you have 4 different boxes b1,b2,b3,b4 then there are 4 ways to put i1 in any of the boxes similarly for i2 there are 4 boxes, similarly i3 can be placed in any of the 4 boxes...... so it becomes 4*4*4*4*4 = 4⁵ = if there k items and n boxes then it will become = n^k