SOLUTION: If there are seven junior students and ten senior students, how many combinations of students can form a committee of six students if at least one student is a senior student.

Question 592783: If there are seven junior students and ten senior students, how many combinations of students can form a committee of six students if at least one student is a senior student.
I thought it was 10C1 x 16C5 , but apparently that's wrong?
Please help me!
Found 2 solutions by scott8148, jim_thompson5910:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
looks okay to me; why do you think it is incorrect?

there must be at least one senior ___ there are 10C1 (or 10) ways to fill this one NECESSARY spot

the remaining 5 spots on the committee may be filled by any combination of the remaining 16 students 16C5

this is a fairly straight-forward solution ___ not sure why it is not offered as one of the choices

textbooks have been known to contain errors...

O.K. , after further thought...

there are 17C6 ways to form a committee ___ (this equals 12376 ___ 10C1 * 16C5 equals 43680 , so something is amiss)

there are 7C6 ways to form a committee with NO seniors

the number of possible committees with at least one senior is ___ 17C6 - 7C6

looking at the first solution, there are duplications in the calculated value
___ eg. take seniors X, Y, and Z
___ if X was the single selection; and Y and Z were part of the final group
___ it would be the same if Y was the single; and X and Z were part of the group

sorry it took so long to figure
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The key word is "at least one student is a senior student"

So you could have

1 senior, 5 juniors
2 seniors, 4 juniors
3 seniors, 3 juniors
4 seniors, 2 juniors
5 seniors, 1 junior
6 seniors, 0 juniors

Does that help?
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