Question

1.

A serial number is to be created for each product that is manufactured. The serial number consists of 2 letters followed by 3 non-zero digits. There are a total of 26 letters in the alphabet.

(a) How many serial numbers are possible if all the letters and non-zero digits CAN'T be repeated?    

(b) How many serial numbers are possible if the letters and non-zero digits can be CAN be repeated?

2.

There are 84 people that have entered into a random drawing that has 3 prizes.

(a) If each prize is different, how many ways can the prizes be awarded?    

(b) If each prize is the same, how many ways can the prizes be awarded?

Answer 1

0 we non-zero choose first three digits and then two letter the serial number is following form. in the 3 digits. 2 letters. a when all the digits and letters can't be repeated. First box have a choices. call nonzero number] second box have 8 choices. ( a number can't be repeated which is filled in first box). Third box have 7 choices. (2 number are filled in first and second box can't be filled in third box) fourth box have 26 choices (there are 26 letters ) Fifth box have 25 choices. Total serial numbers are 9x8 X 7 X 26 X25 = 327600

(b when the non-zero letters and be repeated numbers can 2 3 digits L all have a choices. letters. t all have 26 choices. since non-zero number can be repeated. all first so three box have g choices. and last two box have 26 choices. so in this case total seiral numbers (9)% (26) = 492804