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

Algebra ->  Algebra  -> Permutations -> 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      Log On

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 Algebra: Combinatorics and Permutations Solvers Lessons Answers archive Quiz In Depth

 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)   (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)   (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 combination formula: Start with the combination formula. Plug in and Subtract to get 9 Expand 15! Expand 9! Cancel Simplify Expand 6! Multiply 15*14*13*12*11*10 to get 3,603,600 Multiply 6*5*4*3*2*1 to get 720 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).