MOM 4UI Unit 5 - Day 4 HW - Combinations I 1, Evaluate each of the following: a) ,G b) (74) e) ((9 2) f) 2000 2000 2. a) In how many ways can an elementary school teacher select 4 individuals from a class of 30 students to be in charge of emptying the recycling bins? b) If the class consists of 14 Grade Threes and 16 Grade Four's, in how many ways can these individuals be selected if the group must contain an equal number of Grade Threes and Grade Fours? 3. A committee of 7 is to be chosen at a small school, with a population of 5 teachers and 32 students, Determine the number of possible committees, if a) there are no restrictions b) The committee must contain 3 teachers and 4 students c) There must be at least one teacher d) There can be at most 3 students e) There must be at least one teacher and at least one student. f) Ms. Zhang, a teacher, must be on the committee. 4. A bag contains 12 red jellybeans, 8 blue jellybeans, and 4 yellow jelly beans. Each jelly bean is numbered, 4 jelly beans are selected a) How many combinations are possible? b) Determine the probability that there are 2 red, 1 blue, and 1 yellow jellybeans c) Determine the probability that there are exactly 3 blue jellybeans, () Determine the probability that all the jelly beans are red, 5. In the game of euchre, 5 cards are dealt from a deck that contains only the Aces, Nines, Tens, and Face cards. a) How many euchre hands are possible? b) What is the probability a euchre hand contains exactly 3 hearts? c) What is the probability it contains all red cards? ") What is the probability there are 2 spades, and one card each from the remaining suits? 6. A family of 2 parents and 9 children arrive at a guest house, The guest house has 3 bedrooms, with 6, 3, and 2 beds respectively. Determine the number of combinations of room assignments, if a) there are no restrictions bj both parents must be in the room with 6 bed c) both parents must be in the same room d) the parents must be in different rooms