How many different ways can 3 people carry four rocks in their backpack?

Answer 1

To determine how many different ways 3 people can carry 4 rocks, we can use the "stars and bars" combinatorial method. We treat the rocks as indistinguishable items (stars) and the people as distinct groups (bars). The formula for distributing (n) indistinguishable items into (k) distinct groups is given by (\binom{n+k-1}{k-1}). In this case, (n = 4) (rocks) and (k = 3) (people), resulting in (\binom{4+3-1}{3-1} = \binom{6}{2} = 15) ways.