SOLUTION: I need your help here-please 14. (2 pts) 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

Algebra ->  Proofs -> SOLUTION: I need your help here-please 14. (2 pts) 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       Log On


   

Question 145216This question is from textbook
: I need your help here-please
14. (2 pts) 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? 19 * 7 at a time = 19*18*17*16*15*14*13
I am not that strong in this field. Can you look over this stuff AND get me the answers when it is done so I know where i may have goofed up? This question is from textbook

Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that order does not matter.





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


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

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Start off with a simpler problem where the principle is the same.
Suppose there are a group of 3 candidates to be chosen from 7
applicants. Now write out the possible choices
A,B,C,D,E,F,G are the candidates
Here's all the ones that include A
ABC ACD ADE AEF AFG
ABD ACE ADF AEG
ABE ACF ADG
ABF ACG
ABG
Without repeating myself, heres the ones that include B
BCD BDE BEF BFG
BCE BDF BEG
BCF BDG
BCG
Without repeating myself, heres the ones that include C
CDE CEF CFG
CDF CEG
CDG
Without repeating myself, heres the ones that include D
DEF DFG
DEG
Without repeating myself, heres the ones that include E
EFG
----------------------
These add up to 35 choices
The formula for combinations from 7 chosen 3 at a time is:
7%21+%2F%283%21+%2A+%287-3%29%21%29+=+35
Now for your problem:
19%21+%2F+%287%21+%2A+%2819+-+7%29%21%29+=+50388
Of course, I could be in error, but I hope not