{a} How many different delegations are possible? [b] How many delegations would have all Democrats? {c} How many delegations would have 2 Democrats and 1 Republican? [[1] How many delegations would include at least 1 Republican? Determine whether the statement is true or false, and explain why. The number of combinations of 10 items taken 3 at a time is equal to the number of combinations of 10 items taken 7 at a time. That is, C(10,3) = C(10.7). 2 Decide whether the exercise involves permutations, combinations, or neither, and then solve the problem. There are 7 rotten apples in a crate of 24 apples. (a) How many samples of 4 apples can be drawn from the crate? (b) How many samples of 4 could be drawn in which all 4 are rotten? (c) How many samples of 4 could be drawn in which there are three good apples and one rotten one? 3. Decide whether the exercise involves permutations, combinations, or neither, and then solve the problem. In a club with 12 juniors and 10 seniors, how many 6-member committees can be chosen that have (a) all juniors? (b) 3 juniors and 3 seniors? (c) at least 5 seniors? 4. Decide whether the exercise involves permutations, combinations, or neither, and then solve the problem. A bag contains 9 black, 1 red, and 5 yellow jelly beans; you take 5 at random. How many samples are possible in which the jelly beans are the following (a) all black? (e) 4 black and 1 yellow? (b) all red? (f) 4 yellow and 1 black? (c) all yellow? (g) 4 red and 1 yellow? (d) 4 black and 1 red? 5 Use a tree diagram for the following. a. Find the number of ways 2 letters can be choosen from the set {A, B, C, D ) if order is important and repetition is allowed. b. Reconsider part a if no repeats are allowed. c. Find the number of combinations of 4 elements taken 2 at a time. Does this answer differ from part a or b