Question

A shelf contains n separate compartments. There are r indistinguishable marbles.

In how many ways can the r marbles be placed in the n compartments?

Answer 1

Answer:
`(n!)/(r!(n-r)!)`

ways

Explanation:

Given that a shelf contains n separate compartments. There are r indistinguishable marbles

The marbles are identical so they can be placed in any order.

Let us consider the places available for placing these r marbles

No of compartments available =n

Marbles to be placed = r

Since marbles are identical and order does not matter

number of ways the r marbles can be placed in the n compartments

= nCr

=
`(n!)/(r!(n-r)!)`