Prof. Jeremiah Hower MAD2104 RVC 1211 2/27/2021 Written Homework 7 | Download for quality grades |

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Problem 1. How many words can be made by rearranging aabbccdd, such that no ’a’ appears somewhere to the right of some ’c’? Justify your answer Problem 1 Answer: For this problem, we need ... to change how we view the question being asked. Instead of finding all the different ways 2 c’s are to the left of the 2 a’s, we can take the b’s and d’s and see that by selecting a position for each of them, the places for the a’s and c’s to go is limited to just one option. Thus, we can find all the possible combinations that 2 d’s and 2 b’s can fit into 8 spaces and that will have the same answer as the question being asked. So, first we find all the ways that 2 b’s can be placed into 8 spaces (8C2 = 28) and then we can take the remaining spaces, 6, and find all the ways 2 d’s can fit into those (6C2 = 15). Thus, our final answer is 8C2*6C2 = 420 different ways. Problem 2. We have 4 different boxes and 6 different objects. We want to distribute the objects into the boxes such that no box is empty. In how many ways can this be done? Justify your answer [Show More]

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