User IDs on an old computer system consist of 4 letter sequences from the first

Question

User IDs on an old computer system consist of 4 letter sequences from the first 8 letters of the English alphabet: a, b, c, d, e, f, g, h. Note that the same letter can be used any number of times in the 4 letter sequence. When a new user first registers, an ID is randomly generated (all outcomes equally likely) with the only condition that it is different from the IDs of all previously registered users. (a) How many different IDs are possible for the first registered user? (b) How many different IDs are possible for the second registered user? (c) Jack, Kate and Sam are the only three users of this system. In how many different possible ways can they be assigned IDs?

Explanation / Answer

a) number of different ID's =( for every letter there are 8 choices )=84 =4096

b)number of different ID's for second registered user =4096-1 =4095

c)for first person can have any ID from 4096 ; second from 4095 and third from 4094;

therefore total number of different possible ways =4096*4095*4094=68669153280

please revert for any clarification required.

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