Suppose you have a bike lock with a code that is seven alpha

Suppose you have a bike lock with a code that is seven alpha-numeric characters long. The first three of these are letters, and The remaining 4 of these are numbers. How many different possible codes are there if you can repeat letters and numbers? How many different possible codes are there if you cannot repeat numbers but can repeat letters? How many different possible codes are there if you cannot repeat numbers and cannot repeat letters? Assume that you cannot repeat any letter or number. What is The probability that The letters in The combination are A, B, and C in any order? Assume that you cannot repeat any letter or number. What is The probability that The letters in The combination are A, B, and C in any order? Assume that you cannot repeat any letter or number. What is The probability that The letters in The combination are A, B, and C in any order? Assume that you cannot repeat any letter or number. What is The probability that all The numbers are odd? Assume that you cannot repeat any letter or number. What is The probability that a combination uses only vowels (that is A, E, I, O, or U) or only even numbers?

Solution

A)

There are (26^3) ways for the letters, and 10^4 ways for the numbers.

Thus, a total of (26^3)*(10^4) = 175760000 ways. [ANSWER]

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b)

There are (26^3) ways for the letters, and 10P4 ways for the numbers.

Thus, a total of (26^3)*(10P4) = 88583040 ways. [ANSWER]

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c)

There are 26P3 ways for the letters, and 10P4 ways for the numbers.

Thus, a total of (26P3)*(10P4) = 78624000 ways. [ANSWER]

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d)

There are 26P3 = 15600 ways to choose the letters.

There are 3! = 6 ways to order ABC.

Thus,

P(A, B, C) = 6/15600 = 0.000384615

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