can the professor reasonably ask that no student use the same combination of flowers as another student uses? why or why not?

Let's suppose there are 10 flowers in each arrangement and each student uses all four types of flower. Let the types be A, B, C, D. Now let the corresponding numbers of these flowers be a, b, c, d.

So a+b+c+d=10. If a, b, c, d are the numbers 1, 2, 3, 4 respectively, there will be 10 flowers. But we can arrange the numbers 1 to 4 in 24 distinct ways. We now apply each arrangement to the flowers. For example,  for 1234 we have one flower of type A, two of type B, three of type C, four of type D. For the arrangement 4123, we have four flowers of type 4, one of type B, two of type C, three of type D. Since there are only 15 students and there are 24 possible combinations using this method, no two students need to have the same combination of flowers. So the 24 permutations of the quantities 1 to 4 results in 24 different combinations of 4 types of flower in the flower arrangements, easily accommodating the students' 15 flower arrangements.

answered Sep 24, 2017 by Top Rated User (581,240 points)