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