(Factorial and exponential expressions, such as 10! and 36 3, can be left as the
ID: 3121057 • Letter: #
Question
(Factorial and exponential expressions, such as 10! and 36 3, can be left as they are. You do not need compute the exact values.) l. (10 points Let S {1, 2, 3, 4, 5) a) List all the 2-combinations of S. b) List all the 2-permutations of S. 2. (10 points) How many numbers must be selected from the set {1, 3, 5, 7, 9, 11,13, 15, 17, 19 to guarantee that at least one pair of these numbers add up to 20? 3. (10 points) There are six different candidates for governor of a state. In how many different orders can the names of the candidates be printed on a ballot? 4. (15 points How many permutations of the letters ABCDEFGH contain a) the string ED? b) the string CDE? c) the strings BA and FGH? d) the strings AB, DE, and GH? e) the strings CAB and BED? f) start with AB and end with H f) start with AB or end with H 5. (10 points) Acustomer survey was done on 290 customers. It shows that 228 customers watched film A and 78 watched film B. 34 customers watched neither films. How many customers watched both film A and film B?Explanation / Answer
Multiple questions have been posted. I will answer first two. Please post questions separately if answers for each one of them is required.
1). a) The two combinations essentially means picking two elements from the set in no particular order. So the answer is (1,2), (1,3), (1,4),(1,5), (2,3),(2,4), (2,5),(3,4),(3,5),(4,5).
b) Two permutation is also about picking two elements and then arranging them in order. For example in this case (1,2) is different from (2,1). So the answer is (1,2),(2,1), (1,3),(3,1), (1,4),(4,1),(1,5),(5,1), (2,3),(3,2),(2,4),(4,2), (2,5),(5,2),(3,4),(4,3),(3,5),(5,3),(4,5),(5,4).
2. Notice that no pair of numbers from {1,3,5,7,9} adds to 20. So incase we choose all these five numbers we are not going to get 20 as sum of any two. But now including any other number from {11,13,15,17,19} does result in pairs which add to 20. So to make sure there is at least one pair such that the sum of two numbers is 20 we have to select at least 6 numbers. So the answer is 6.
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