How to Count Combinations with Repetition Using COMBINA

COMBINA counts choices where items can repeat — ice-cream scoops, donut boxes and any “pick as many as you like” menu.

You will learn to

• Count choices when repeats are allowed
• Count choices that contain at least one repeat
• Count boxes that include at least one of every kind

How it works

COMBINA(number, number_chosen) counts the ways to choose k items from n kinds when the same kind can be picked more than once and order does not matter. A 3-scoop cup from 8 flavours has =COMBINA(8,3) = 120 possibilities, compared with =COMBIN(8,3) = 56 if every scoop must be different.

COMBINA(n,k) equals COMBIN(n+k-1,k). A handy trick: to require at least one of every kind, put one of each in the box first and count the rest — =COMBINA(6,12-6) for a 12-donut box from 6 kinds.

=COMBINA(B2,C2)