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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.
How many ways can a student select five questions from an exam containing 12 questions if he must answer the last question?
330 ways. Once we know he must answer the last question, the issue is really one of choosing 4 questions from the first 11 questions on the exam. There are 11 ways to choose the first question, 10 ways to choose the second, 9 ways to choose the third, and 8 ways to choose the fourth, so that would be 11*10*9*8... but the order of the questions doesn't matter. So we divide by the number of ways to rearrange the 4 questions (4*3*2*1=24), to get 330.
A student has an exam with 30 questions. They are to select 10 of these questions to answer. In how many ways can they complete this exam?
they can complete this exam 300 ways
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 in which a student can choose 5 out of 9 books if 2 books are compulsory?
Two books are compulsory, so the student really wants to know how many ways he can pick 3 out of 7. That is 35.
A test instructs you to answer 2 of the next 5 questions how many ways can you choose 2 questions to answer?
Five (5) multiply by (*) Four (4) = Twenty (20).
In how many ways may a student answer an 8 question true or false exam if he always marks half the questions as true?
16
There are 7 seniors on student council. two of them will be chosen to go to an all-district meeting. How many ways are there to choose the students who will go to the meeting?
Combination; number of ways = 21
How many ways 3 students can sit in 3 chairs?
The first student has 3 chairs to choose from. Once he has mad the choice, the second student has 2 chairs to choose from. And the last student only has 1 choice, so 3 x 2 x 1 = 6 ways.Here are the six ways. For ease, call the students A, B, and C:ABCACBBACBCACABCBA
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 can students benefit from essay questions?
An essay question can benefit a student in two ways: It can encourage the student to think more clearly, as to express the idea in writing, and hence it can also sharpen the student's writing skills.
How many ways can you match 12 questions with 12 answers?
144 ways
