SOLUTION: In a 10-item Mathematics problem-solving test, how many ways can you select 5 problems to solve? How many ways can you select the 5 questions if you are required to answer question

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Question 1066088: In a 10-item Mathematics problem-solving test, how many ways can you select 5 problems to solve? How many ways can you select the 5 questions if you are required to answer question number 10?
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
Part a)
Since it appears that the order does not matter (we are just choosing any 5 at once), then we are using a combination. A couple of different ways to compute this.
You can use the nCr button on your calculator, but I will do it using the formula.
So nCr = n%21%2F%28%28n-r%29%21%2A+r%21%29
We are finding 10 C 5 = +10%21+%2F%285%21+%2A+5%21%29+
10! is quite large, so let's try to do some simplification.


%2810%2A9%2A8%2A7%2A6%29%2F%285%2A4%2A3%2A2%2A1%29
%28cross%2810%29%2A9%2A8%2A7%2A6%29%2F%28cross%285%29%2A4%2A3%2Across%282%29%2A1%29
%289%2A8%2A7%2A6%29%2F%284%2A3%29
%28cross%289%293%2Across%288%292%2A7%2A6%29%2F%28cross%284%29%2Across%283%29%29
and 3 * 2* 7 * 6 is highlight%28252%29.
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Part b)
10 is fixed so we really only have 9 questions and we are choosing 4.
So 9 C 4 =
%289%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%28%285%2A4%2A3%2A2%2A1%29%284%2A3%2A2%2A1%29%29
%289%2A8%2A7%2A6%29%2F%284%2A3%2A2%2A1%29

So 3 * 7 * 6 = highlight%28126%29
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Finally, Google will do it for you as well.
10 choose 5 : https://www.google.com/#q=10+choose+5
9 choose 4 : https://www.google.com/#q=9+choose+4