MATH 61 Midterm: MATH 61 Exam 4
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Midterm 2 review (test on 12 november 2008) The binomial coe cient (cid:0)n k(cid:1) is used to count the number of k-element subsets of an n-element set. The term binomial coe cient comes from the binomial the- orem: (a + b)n = Various properties involving binomial coe cients can be proved by using the above relationship for appro- priate choices of a and b. binomial coe cients satisfy some important properties: k(cid:19) = (cid:18) n (cid:18)n n k(cid:19), n. Xi=0 k (cid:19), k 1(cid:19) +(cid:18)n 1 k(cid:19) = (cid:18)n 1 (cid:18)n k + 1(cid:19). k(cid:19) = (cid:18)n + 1 (cid:18) i. The binomial coe cients can be arranged in a trian- gular pattern known as pascal"s triangle. The rst few rows of pascal"s triangle are given below. (cid:0)n k(cid:1) k=0 k=1 k=2 k=3 k=4 k=5 k=6 n=0 n=1 n=2 n=3 n=4 n=5 n=6.
