Question 927995: There are ten questions on a test. The instruction say that only seven of the questions are to be answered. How many ways can the seven to be answered be selected? Hint: The order in which the seven questions are answered is not important. All that matters is which seven are eventually answered.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! This is the same as asking "How many ways are there to pick 3 questions to NOT answer". This is easier because 3 is less than 7. Let's say we have 3 slots for the 3 questions we don't answer.
10 problems to choose from for slot 1
9 problems to choose from for slot 2
8 problems to choose from for slot 3
10*9*8 = 720 ways to pick 3 problems where order matters
Divide by 3! = 3*2*1 = 6 to get 720/6 = 120
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There are 120 ways to select 3 problems that will NOT be attempted. The other 7 will be done.
So there are 120 ways to pick 7 problems where order doesn't matter. The final answer is 120
Notice how 10 C 7 = 10 C 3 = 120 and how this symmetry shows up in Pascal's Triangle.
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