1) In how many ways can we write 16 as the sum of three distinct positive integers? [Note: Assume that 1 + 11 + 4 is the same as 4 + 1 + 11

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1) In how many ways can we write 16 as the sum of three distinct positive integers? [Note: Assume that 1 + 11 + 4 is the same as 4 + 1 + 11.] 

2. Two regular, fair dice are rolled. We add the two numbers on the top faces. How many different sums are possible? 

 3. A group of six strangers sat in a circle, and each one got acquainted only with the person to the left and the person to the right. Then all six people stood up and each one shook hands once with each of the others who was still a stranger. How many handshakes occurred?  

 4. How many odd, nonrepeating, three-digit numbers can we write using only the digits 0, 1, 2, an 3?

5. Until 1995, the rules for three-digit area codes in the U.S. were as follows: (i) The first digit could not be 0 or 1. (ii) The second digit had to be 0 or 1. (iii) The third digit had no restrictions. a) How many area codes were possible? b) In 1995, the restriction on the second digit of area codes was removed. How many area codes are possible?