SOLUTION: This is the last problem that i missed on my exam please help me .. so I will have it straigh for my final. thank you T-Aun How many different ways are there for an admis

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Question 199877: This is the last problem that i missed on my exam please help me .. so I will have it straigh for my final. thank you T-Aun



How many different ways are there for an admissions officer to select a group of 6 college candidates from a group of 15 applicants for an interview?


Found 2 solutions by rfer, jim_thompson5910:
Answer by rfer(12730) About Me  (Show Source):
You can put this solution on YOUR website!
I believe that the first choice is 1 out of 15, second pick is 1 out of 14, and so on.
1/15x1/14x1/13x1/12x1/11x1/10=3,603,600

Answer by jim_thompson5910(28715) About Me  (Show Source):
You can put this solution on YOUR website!
Unfortunately, the previous solution is incorrect. Why? They're not looking for a probability, they just want to know the number of possible combinations.




We could use the counting principle to solve this problem, but we'll have overlap and the sample space is far too large. So let's do it this way:


In this case, order does NOT matter since the candidates have no rank over one another (ie one isn't president or secretary).


Since order does not matter, we must use the <a rel=nofollow HREF=http://www.mathwords.com/c/combination_formula.htm>combination formula</a>:


n%21%2F%28n-r%29%21r%21 Start with the combination formula.


15%21%2F%2815-6%29%216%21 Plug in n=15 and r=6


15%21%2F9%216%21 Subtract 15-6 to get 9


%2815%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F9%216%21 Expand 15!


Expand 9!


Cancel


%2815%2A14%2A13%2A12%2A11%2A10%29%2F6%21 Simplify


%2815%2A14%2A13%2A12%2A11%2A10%29%2F%286%2A5%2A4%2A3%2A2%2A1%29 Expand 6!


3603600%2F%286%2A5%2A4%2A3%2A2%2A1%29 Multiply 15*14*13*12*11*10 to get 3,603,600


3603600%2F720 Multiply 6*5*4*3*2*1 to get 720


5005 Reduce.


So 15 choose 6 (where order doesn't matter) yields 5,005 unique combinations


This means that there are 5,005 different ways to select a group of 6 college candidates from a group of 15 applicants for an interview (where the order of the candidates doesn't matter).