Question

In how many ways can n balls be randomly distributed in n cells? What will be the number of ways if it is specified that each cell is to be occupied?

Answer 1

Answer:

n^n

n!

Step-by-step explanation:

Hi,

Number of ways that n balls can be randomly distributed in n

cells:

Consider Ball 1, we can place it in any of the given n cells, hence

there are n ways, similarly second ball also could be placed in

any of the given n cells and so on continuing.. Total number of

ways this distribution can happen will be

n*n*n*......n times which is n^n .

If it is specified that each cell is to be occupied:

Firstly, we'll distribute 1 ball to each cell this can be done in n!

ways. First Ball could be in any of the n cells, then the second in

any of (n -1) cells leaving the one cell that is occupied by the first

ball and then the third could be placed in any of (n - 2) cells and

so on.... we get total number of ways this distribution could

happen are n*(n-1)*(n-2)*....*2*1 = n!

Hope, it helps !