Finite Mathsection 6.5 CombinationsNotation: P(n, r) = # of ways to arrange r distinct items in order. C(n, r) = # of ways to select r distinct items without order.Thm P(n, r) = n 1) n 2) n 3).... (n(n) ( ( ( (r 1) )Def n = (n) ( ( ( nx n 1) n 2) n 3)....(2)(1) (where ) −Thm C(n, r) = = = ........... n, rnrn r ( 1234 k(n)((( (xxxnr)n1)n2)n3) nr+1) (where , r n)−ŸEx1, An SMC Club has 6 students. Find the number of ways to select (a) 1 President and 1 Vice President. P(6, 2) (b) 2 representatives. C(6, 2) (c) 1 President, 1 VP, and 1 Treasurer. P(6, 3) (d) 3 representatives. C(6, 3)Ex2, At a restaurant, there are 5 veg, 4 fruits, and 3 meats. How many ways to select (a) any 2 (distinct) items (b) any 2 items from fruits or meats. (c) 3 items, 1 veg, 1 fruit, 1 meat. (d) 4 items, 2 veg, 1 fruit, and 1 meat. (e) 4 items, any 2 items from veg or fruits and 2 meats.Ex3, Ice cream store is 4 blocks east and 3 blocks north of your house. Assuming that there are streets at every block, how many ways are there from your house to the ice cream store?Pascal's ˜Binomial Theorem n1 n(A+B) = A + A B+ A B + A B + .......+ AB + Bnn n n n n01 2 3n23 nn1 n2 n3 n1n = A + n A B+ A B + A B + .......+ n AB + Bnn1 n2 n3 n1n n( n( (23n1) n1)n2)23xEx4, Expand (2x 3y)5Ex5, Find the coefficient of in the expansion of xy (x
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