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The first question can be any one of the 10. For each of these . . .
The second question can be any one of the remaining 9. For each of these . . .
The third question can be any one of the remaining 8.
Total number of ways to choose 3 questions = (10 x 9 x 8) = 720 ways.
But the same 3 questions can be chosen in any one of 6 sequences.
So the number of different sets of 3 questions is only 720/6 = 120 .
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A student is told to work any 8 out of 10 questions on an exam in how many different ways can he complete the exam?
100,000,000 ways
How many ways can 6 students desks be arranged in a row?
This is 6! {factorial} = 6 x 5 x 4 x 3 x 2 x 1 = 720. The way this works: take student A, who can choose any of the 6 desks, then for each of those 6 choices that student A makes, student B has 5 desks to choose from, after that choice has been made, student C has 4 desks to choose from, ... until the last student has only one to choose from.
How many ways can a student select 7 questions from an exam containing 11 questions if he must answer the last question?
If he must answer the last question, he effectively needs to select 6 from 10. This can be done in 10C6 = 10*9*8*7/(4*3*2*1) = 210 ways.
How many ways can you choose 5 out of 9?
Nine
If there are ten questions on a true or false how many possible ways to answer?
210 or 1024 ways.
