A Masters student in Sales (me) is conducting a sales motivation census. Each question has 16 factors of motivation. The respondent has 16 points available to score 'relative importance' against each or any of the factors. Every score must add up to 16. The respondent is allowed to score ‘all 16 points against one factor’ or ‘1 point against all 16 factors’ or any combination in between; however the total points scored must always add up to 16.

Questions:-

1. How many unique answer combinations are there?

2. How many unique answer permutations are there?

3. If the census contained 10 similar questions and a million salespeople took part. What's the probability of 2 people scoring exactly the same answers throughout the survey?

- Clue! I've calculated the question long hand on smaller 'factors' and 'points' and spotted a trend (albeit I don't understand the relationship) Try the same question with only 2 factors adding up to 2 points.

then 3 factors adding up to 3 points

then 4 factors adding up to 4 points etc.

The answer must include the formulas used and application of workings.

1st correct answer will receive an acknowledgement in my Master’s dissertation + a signed copy.