SOLUTION: There are 10 students from whom 4 are going to be chosen to represent their club at a meeting. If, Sue, Mark, or John, but only one of them must be chosen, in how many ways can the

Algebra ->  Permutations -> SOLUTION: There are 10 students from whom 4 are going to be chosen to represent their club at a meeting. If, Sue, Mark, or John, but only one of them must be chosen, in how many ways can the      Log On


   

Question 1099905: There are 10 students from whom 4 are going to be chosen to represent their club at a meeting. If, Sue, Mark, or John, but only one of them must be chosen, in how many ways can the students be chosen to go to the meeting?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Notice that the problem is different if you change "MUST" to "CAN":

There are 10 students from whom 4 are going to be chosen to
represent their club at a meeting. If, Sue, Mark, or John,
but only one of them MUST be chosen, in how many ways can
the students be chosen to go to the meeting?
That's (3 choose 1) AND (7 choose 3)

(3C1)(7C3) = (3)(35) = 105 ways.

However if the problem were:

There are 10 students from whom 4 are going to be chosen to
represent their club at a meeting. If, Sue, Mark, or John,
but only one of them CAN be chosen, in how many ways can
the students be chosen to go to the meeting?
That's [(3 choose 1) AND (7 choose 3)] OR [(3 choose 0) AND (7 choose 4)]

(3C1)(7C3) + (3C0)(7C4) = (3)(35) + (1)(35) = 105 + 35 = 140 ways.

Edwin