A security code is made up of 2 letters of the alphabet, followed by 4 digits (0

Question

A security code is made up of 2 letters of the alphabet, followed by 4 digits (0-9). a. How many codes are possible if repetition is NOT allowed? b. How many codes are possible if repetition is NOT allowed and the letters I and O are not allowed and the digits 0 and 1 are not allowed? You need to create a 4-digit PIN for your Visa Debit card. a. How many PINs are possible if the first digit must be a 5 and repetition is NOT allowed? b. How many PINs are possible if the first digit must be a 5 and repetition of consecutive digits is NOT allowed? (So for example, a PIN of 5757 or 5785 would be allowed, but a code of 5578 or 5778 or 5788 would NOT be allowed.)

Explanation / Answer

Ques 1

a) If repition is not allowed, no. of codes = 26*25*9*8*7*6= 1965600 (since any of 26 albhabet can be used in 1st place, any of the alphabet except the one already used can be used in 2nd place)

b) If I &O and numbers 0,1 are not allowed = 24*23*7*6*5*4=463680( Since I & O cannot be used, alphabet only amongst rest 24 can be used for 2nd place)

Ques2.

a. If 5 is laready used in 1st place and repetition is not allowed, then pin can be formed in 8*7*6 =336 ways

b. If repetition for consecutive no.s is not allowed then, 2nd place can have any 8 no.s except 5

3rd place can have any 8 no.s except the no. used in 2nd place

4th place can have any of the 8 no.s except the no. used in 3rd place

So no. of ways= 8*8*8= 512 ways

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