how many four-digit lock combinations can be made for thefollowing? a. the first

Question

how many four-digit lock combinations can be made for thefollowing? a. the first digit is a 1 or a 2, and all the digits areunique. b. the first digit is a 1 or a 2, and digits may berepeated. c. the first digit is any number but 0, and the digits may berepeated. how many four-digit lock combinations can be made for thefollowing? a. the first digit is a 1 or a 2, and all the digits areunique. b. the first digit is a 1 or a 2, and digits may berepeated. c. the first digit is any number but 0, and the digits may berepeated.

Explanation / Answer

a) first digit has to be a 1 or a 2: 2 possibilities out of 10 other digits are unique: 10 possibilities. I assume that the digits can be 0,1,2,3.... 9, which makes 10possibilities You can multiply these possibilities: 2*10*10*10= 2000 possibilities b) I do not understand the situation The first digit has to be again a 1 or 2: 2 possibilities next, everything has to be a 1 if the first digit is a 1? (and thesame for a 2?) Then, there are 2 possibilities: 2 2 2 2 1 1 1 1 c) Four the first digit, there are 9 possibilities (1,2,3 ... 9) The digits has to be repeated again, so 1 1 1 1, 2 2 2 2 ....9 9 9 9 ? Then, there are 9 possibilities Note, I am not sure of I understand b and c correctly. You can senda private message if my interpretation is incorrect. Good Luck further :)

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