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.Com
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) (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:
Start with the given formula
Plug in and
Subtract to get 12
Expand 19!
Expand 12!
Cancel
Simplify
Expand 7!
Multiply 19*18*17*16*15*14*13 to get 253,955,520
Multiply 7*6*5*4*3*2*1 to get 5,040
Now divide
So 19 choose 7 (where order doesn't matter) yields 50,388 unique combinations
Answer by josmiceli(19441) (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:
Now for your problem:
Of course, I could be in error, but I hope not
RELATED QUESTIONS
(2 pts) How many different ways are there for an admissions officer to select a group of... (answered by stanbon)
How many different ways are there for an admissions officer to select a group of 7... (answered by stanbon)
How many different ways are there for an admissions officer to select a group of 7... (answered by checkley77)
I am not that strong in this field. Can you look over this stuff AND get me the answers... (answered by Alan3354)
How many different ways are there for an admissions officer to select a group of 6... (answered by checkley77)
How many different ways are there for an admissions officer to select a group of 6... (answered by stanbon)
How many different ways are there for an admissions officer to select a group of 6... (answered by edjones)
How many different ways are there for an admissions officer to select a group of 6... (answered by rfer)
How many different ways are there for an admissions officer to select a group of 6... (answered by stanbon)