Question

3. (a) (3 pts.) Determine in how many ways one can place twelve indistinguishable balls in six boxes in such a way that none of the boxes is empty. (b) (3 pts.) Repeat the exercise from part (a) with r balls and n boxes, where r > n.

Answer 1

b)

The general formulae for ways to distribute n identical things in r groups such that no group is empty is:

^n+r-1C_{r ­­­}

where n > r

a)

when n = 12 and r = 6

using the above formulae: we get,

^12+6-1C₆ = ¹⁷C₆ = 12376