Usernames on a computer system consists of 3 letters (A through Z) followed by 3

Question

Usernames on a computer system consists of 3 letters (A through Z) followed by 3 digits (0 through 9). Letters are not case sensitive. Letters and digits may appear more than once in a name (for example, xax323 is a valid username) How many user names of this type are there? Joe has user name TPK635, but he can only remember the 3 letters K, T, P (but the order of the letters nor the 3 digits used in the username) If he picks a name at random from those consistent with his memory, what is the probability that he get the correct username TP K635? Joe from part (b) also remebers that the 3 digits user e are 3, 5, 6 the order, and he picks a name at random from those consistent with his memory, what is the probability that he get the correct username TPK635?

Explanation / Answer

Answer:

2a).

Number of user names = 26*26*26*10*10*10

=17576000

b).

permutation of 3 letters

3P3=6

Number of user names = 6*10*10*10 =6000

The required P =6000/17576000

=0.000341375

c).

permutation of 3 digits =3P3=6

Number of user names = 6*6=36

The required P =36/17576000

=0.00000205

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