4. If 3 letters are chosen from A, B, C, D and E such that the repetition is not allowed. How many ways this can be done?
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?
3. Consider rearranging the letters in the word "FATHER" (a) Find the number of 6 letter "words that can be formed by considering all possible permutations of the letters in the word "FATHER" (b) How many of these words begin with "F" and end with "R"? (c ) What is the probability of forming a six letter word that begins with F" and ends with "R" by randomly rearranging the letters in "FATHER?
5. A presidential candidate plans to begin her campaign by visiting the capitals in 3 of 48 states. What is the probability that she selects the route of three specific capitals? Is it practical to list all of the different possible routes in order to select the one that is best? P(she selects the route of three specific capitals)=____ (Type an integer or a simplified fraction.) Is it practical to list all of the different possible routes in order to...
There are 10 letters - a, b, c, d, e, f, g, h, n, g. I have to arrange them in a way that "a" wouldn't be near "c" and also "a" wouldn't be near "g" How many possible combinations are possible? How to solve it mathematically?
5. Eight letters {A, B, C, D, E, F,G,H} appear in a 100 letter length message with the following frequencies: 22, 6, 13, 19, 2, 9, 25, 4. (a) Use Huffman tree to design an optimal binary prefix code for the letters. (b) What is the average bit length of the message after apply codes designed in (a) to the message? [20 marks]
Given the unordered array: [0] [1] [2] [3] [4] [5] C R D E P T List all the letters, in the order stored, after this array is converted to a heap. For example, the original array would have been listed as: CRDEPT
Consider the following graph: b a 15 5 10 3 e 6 d 30 C 5 6 2 i j h f 4 k (c) (4 pts.) Show all the articulation points in the graph if exist
Question 33 Consider the following code segment. String letters - ("A", "B", "C", "D"), ("E", "P", "G", "1"), ("I", "J", "K", "L"}}; for (int col = 1; col < letters[0].length; col++) for (int row - 1; row < letters.length; row++) System.out.print(letterstrow][col] + " "); System.out.println(); What is printed as a result of executing this code segment? AET PJ DHL G J K L PJ GK
numbers are formed using all the digits 1, 2, 3, 4 ,5, 7, 8,9 without repetition. Determine the number of possible permutations in the following case. Show all steps in factorial form before final answers. 9 is before 1 but not necessarily adjacent to it. i.e, 912345678 or 234956178