SOLUTION: How many different ways are there for an admissions officer to select a group of 7 college candidates from a group of 19 applicants for an interview? Can you help me with this

Algebra ->  Permutations -> SOLUTION: How many different ways are there for an admissions officer to select a group of 7 college candidates from a group of 19 applicants for an interview? Can you help me with this       Log On


   

Question 187873: How many different ways are there for an admissions officer to select a group of 7 college candidates from a group of 19 applicants for an interview?
Can you help me with this problem? I know the answer is 50388, but if I do it this way it does not come out right? What am I doing wrong? HELP please!!!
19*18*17*16*15*14*13 =253955520/7 =36279360 from here I know I am a mess.
Thanks for any help, I am pulling my hair out.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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:


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



19%21%2F%2819-7%29%217%21 Plug in n=19 and r=7



19%21%2F12%217%21 Subtract 19-7 to get 12


Expand 19!



Expand 12!




Cancel



%2819%2A18%2A17%2A16%2A15%2A14%2A13%29%2F7%21 Simplify. Note: you forgot to divide by 7! (you just divided by 7)


Expand 7!
%2819%2A18%2A17%2A16%2A15%2A14%2A13%29%2F%287%2A6%2A5%2A4%2A3%2A2%2A1%29



253955520%2F%287%2A6%2A5%2A4%2A3%2A2%2A1%29 Multiply 19*18*17*16*15*14*13 to get 253,955,520



253955520%2F5040 Multiply 7*6*5*4*3*2*1 to get 5,040



50388 Now divide



So 19 choose 7 (where order doesn't matter) yields 50,388 unique combinations