In a preschool class of n, exactly n1 children are needed foractivity 1, n2 for activity 2, and n3 for activity 3. Luckily n =n1 + n2 + n3. The teachers want to know in how many distinct waysthe children can be assigned into these activities. (Twoassignments are distinct if at least one student is in a differentactivity in each.) (a) They figure they could start by lining upthe children arbitrarily. How many different line-ups are possible?(b) They then take the first n1 for activity 1, the next n2 foractivity 2, and the rest for activity 3. How many differentline-ups will create the exact same assignment of children toactivities? (c) Use your answers from (a) and (b) to deduce thetotal number of distinct assignments.
