1. (7 points) Let X = {A, B, C, D, E, F, G, H). a. (a poin) How many strings ove
ID: 3146412 • Letter: 1
Question
1. (7 points) Let X = {A, B, C, D, E, F, G, H). a. (a poin) How many strings over X have length s? b. (1 point) How many strings over X of length 5 do not contain the letter A? c. (1 point) How many strings over X of length 5 contain the letter A? d. (1 point) How many strings over X of length 5 do not contain the letter A or do not contain the letter B? f. (a point) How many strings over X of length 5 do not contain the letter A nor a repeated letter? E. ( point) How many strings over X of length s contain the letter A but not a repeated letter?Explanation / Answer
(According to Chegg policy, only four subquestions will be answered. Please post the remaining in another question)
X = {A, B, C, D, E, F, G, H}
a. Every letter has 8 choices.
=> Number of 5 length strings = 85 = 32768.
b. Since the strings do not contain A, they have 7 choices.
=> Number of 5 length strings without A = 75 = 16807.
c. Number of 5 length strings that contain A
= Number of 5 length strings - Number of 5 length strings without A
= 85 - 75
= 32768 - 16807
= 15961.
d. Number of 5 length strings without A = 75 = 16807
Number of 5 length strings without B = 75 = 16807
Number of 5 length strings without A and B = 65 = 7776
Number of 5 length strings without A or B = 16807 + 16807 - 7776 = 25838.
(Note: If only one of the two events i.e A not being there or B not being there has to happen, the answer is 25838 - 7776 = 18062.)
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