Bogart 1.4 #1.

Remember that we can write n as a sum of n ones. How many plus signs do we use? Question: In how many ways may we write n as a sum of a list of k positive numbers? Such a list is called a composition of n into k parts. For example, there are three different ways can we write n=5 as a sum of a list of k=3 positive numbers: - 1+1+3 = 5 - 1+3+1 = 5 o 3+1+1 = 5 Notice that we want to count all three sums, even though they all use two "1's" and one \"3". HINT: How many ways can you insert two \"+" signs into the list 1 1 1 1 1