Answers

1. Answer:

   There are 9 possible thousands digits, because 0 cannot be the leading digit.

   There are 2 possible ones digits, 0 and 5.

   If the ones digit is 5:

   There are 5 possible thousands digits: 1, 2, 3, and 4.For each possible thousands digit, there are 5 possible hundreds digits. (We used one of the digits above to be the thousands digit, but 0 is a possible hundreds digit.)For each possible pair of thousands-and-hundreds digits, there are 4 possible tens digits.

   So there are 5 x 5 x 4 = 100 possible 4-digit numbers that end in 5 with no repeated digit and no digit larger than 5.

   If the ones digit is 0:

   There are 5 possible thousands digits.For each possible thousands digit, there are 4 possible hundreds digits.For each possible pair of thousands-and-hundreds digits, there are 6 possible tens digits.

   So there are 5 x 4 x 6 = 120 possible 4-digit numbers that end in 0 with no repeated digit and no digit larger than 5.

   100+120=220

   Answer: 220 possible numbers.

   Log in to Reply