Question

1An identification code is to consist of 2 letters followed by 5 digit. Determine the fallowing?

1a) how many different codes are posible if repetition is permitted?

1b) how many different codes are possible if repetition is not permitted, but the first 2 letters must ve the same letter?

1c) how many different codes are possible if the first letter must be, P, Q, R, S, T, and repetition for everything else is not permitted?

Answer 1

a) Number of different codes that are possible here given that repetition is permitted is computed here as:

= 262 * 105

= 67600000

Therefore 67600000 codes are possible here.

b) Given that repeition is not allowed, but first 2 letters should be same, the number of codes here is computed as:

= Number of ways to choose one of the 26 letters * Number of permutation of 10 digits taken 5 at a time

= 26*10*9*8*7*6

= 786240

Therefore 786240 codes are possible here.

c) Number of codes possible here is computed as:

= Number of ways to choose the first letter * Number of ways to choose second letter from remaining 25 letters * Number of permutation of 10 digits taken 5 at a time

= 5*25*(10! / 5!)

= 3780000

Therefore 3780000 codes are possible here.