Find the number of times the player should throw so that his probability of hitting the bull’s-eye at least once is 0.5.

Question

Fred needs to choose a password for a certain website. Assume that he will choose an 8-character password, and that the legal characters are the lowercase letters a, b, c, ..., z, the uppercase letters A, B, C, ..., Z, and the numbers 0, 1, . . ., 9. (a) How many possibilities are there if he is required to have at least one lowercase letter in his password? (b) How many possibilities are there if he is required to have at least one lowercase letter and at least one uppercase letter in his password? (c) How many possibilities are there if he is required to have at least one lowercase letter, at least one uppercase letter, and at least one number in his password?

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Chapter 1.8, Problem 77P

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Find the number of times the player should throw so that his probability of hitting the bull’s-eye at least once is 0.5.

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Fred needs to choose a password for a certain website. Assume that he will choose an 8-character password, and that the legal characters are the lowercase letters a, b, c, ..., z, the uppercase letters A, B, C, ..., Z, and the numbers 0, 1, . . ., 9. (a) How many possibilities are there if he is required to have at least one lowercase letter in his password? (b) How many possibilities are there if he is required to have at least one lowercase letter and at least one uppercase letter in his password? (c) How many possibilities are there if he is required to have at least one lowercase letter, at least one uppercase letter, and at least one number in his password?

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