Question

Suppose each user of a high-performance supercomputer is randomly assigned a unique ID consisting of three letters from the English alphabet followed by 3 non-repeating digits between (and including) 0 and 9. Here are some sample IDs: AAA123, ZYZ456, YAM019, etc. (Note: ABC242 is not allowed since "2" is repeated).

a) How many IDs can be made in this fashion?

b) Determine the probability that an ID randomly assigned in this fashion ends with "123".

Answer 1

a.)Total alphabets=26 (A,B.....Z), total digits=10(0,1,2......9)

Alphabets can be repeated but digits cant

Hence

Number of Possible IDs=26*26*26*10*9*8=12654720

b.)

probability that an ID randomly assigned in this fashion ends with "123"=(26*26*26)/12654720=0.00139

Hence

Ans: 0.0014