Consider the set of integer numbers from 0 to 9, that is {0, 1, 2, 3,...

Consider the set of integer numbers from 0 to 9, that is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. Bob wishes to use these numbers to create a 7-digit password to secure his new laptop. Note that each number can appear in any position (for example, 0 can be the first number in the password). (a) Find the number of 7-digit passwords that are possible. (b) Find the number of 7-digit passwords with distinct digits. (c) Find the number of 7-digit passwords that contain exactly three 4s (that is, inside the password the number 4 appears exactly three times). (d) Find the number of 7-digit passwords that do not contain any 1 (that is, inside the password the number 1 never appears). (e) Find the number of 7-digit passwords that contain at least one 6 (that is, inside the password the number 6 appears at least once). (f) Find the number of 7-digit passwords that contain exactly two 6s and one 5 (that is, inside the password the number 6 appears exactly twice and the number 5 appears exactly once). (g) Find the number of 7-digit passwords that contain exactly two 4s and three 2s (that is, inside the password the number 4 appears exactly twice and the number 2 appears exactly three times).

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Manojponduru answered 1 year ago

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