Question 282431: Two of seven finalists will be selected and awarded $10,000 scholarships. In how many different ways can this final selection be made? Answer by solver91311(24713) (Show Source):
Since the two prizes to be awarded are the same value, the order of selection does not matter. Hence, you need the number of ways to select 2 things from 7 things.
The number of ways to select things from things where order doesn't matter is:
Just substitute and do the arithmetic.
Super Deluxe Double Plus Extra Credit: What is the difference in your answer if, instead of two $10,000 prizes, the committee was awarding a $13,000 prize and a $7,000 prize?
