16 Topic : COMBINATIONS, BINOMIAL THEOREM TIME : 4 X 45 minutesSTANDARD COMPETENCY : 1. To use the statistics rules, the rules of counting, and the characteristic of probability in problem solving. BASIC COMPETENCY:1.5 To use the rules of multiplication , permutation, and combination in problem solving. In this chapter, you will learn about: •To arrange the rules of combination of robjects from ndifferent objects. •To use the rules of combination. •To use the rules of Binomial Newton to determine the expansion ofi (nba+D. COMBINATIONS Having studied permutations where the order of each object is important, let us turn our attention to combinations. A combinationis any selection of objects where the order of the objects is immaterial (of no concern) For example, the different (ordered) permutations ABC and CAB are considered as the same combination when we disregard the order of the letters and realize that both contain the same three letters. Consider the permutations of 2 people from 4 people, P,Q,R, and S. We have learned that there are 4P2= 12 such permutations. Permutations (order important) Combinations (order not important) ∴The combinations of 2 people from 4 people are … combinations PQ QP PQ PR RP PR PS SP PS QR RQ QR QS SQ QS RS SR RS Consider the permutations of 3 people from 4 people, P,Q,R, and S. We have learnt that there are ….P….= ….. such permutations. Worksheet 3rd
17 Permutations (order important) Combinations (order not important) ∴The combinations of 3 people from 4 people are … combinations PQR QPR RQP PRQ QRP RPQ PSQ ….. ….. ….. .…. ….. PRS ….. ….. ….. .…. ….. QRS ….. ….. ….. .…. ….. In general, the number of combinations of robjects from ndifferent objects is (29!!!rCCrnnrKKK-==Example 19 From 8 students shall be chosen 3 students for a visit to Jakarta. Find the number of possibilities in choosing the three students. PQR …… …… …… Example 20 A committee of 5 members is to be selected from 6 seniors and 4 juniors. Find the number of ways in which this can be done if a. there are no restrictions, b. the committee has exactly 3 seniors, c. the committee has at least 1 junior.