Question
answer clearly and correctly please! I will not accept wrong answers!
Consider the following set {a, b, c, d} In how many different orders can this set be arranged? List all the possible arrangements of this set in dictionary order. What is the 15th permutation, that is, the 15th item on the list you created in step b? Write a Pseudocode algorithm for constructing any specified permutation of these four letters, without constructing or referring to the list. Verify that your algorithm correctly constructs the 15th permutation that you identified in part c. Hint: You may want to start with the example included at the end of this document, of a Pseudocode algorithm to identify the kth permutation of a set of 3 objects, and modify it to do 4 objects. Or you may do your own from scratch, if you prefer. This example is not the most efficient version, or the most general, but it does perform correctly in all cases. A fair coin is tossed four times. List the entire sample space for this experiment. Use your sample space from part (a) to answer the following questions: What is the probability that it turns up heads every time? What is the probability of at least 2 heads? What is the probability of two tails in a row? A single card is drawn from a standard 52-card deck. What is the probability of getting: A 10 or an Ace? An Ace or a diamond?
Explanation / Answer
4) a) 4! = 4*3*2*1 = 24
b) 1 ABCD
2 ABDC
3 ACBD
4 ACDB
5 ADBC
6 ADCB
7 BACD
8 BADC
9 BCAD
10 BCDA
11 BDAC
12 BDCA
13 CABD
14 CADB
15 CBAD
16 CBDA
17 CDAB
18 CDBA
19 DABC
20 DACB
21 DBAC
22 DBCA
23 DCAB
24 DCBA
