For an international Mathematics Olympiad, country D will send six delegates in total — two will be supervisors and four will be contestants. There are 210 ways in which the six delegates can be chosen and there are seven candidates competing for the four contestants’ places available. How many candidates are competing for the two supervisors’ slots available? Choose the correct choice from the following choices.
A) 1  B) 2  C) 3  D) 4  E) 5
Option A wrong as 2 supervisor need to be selected.   Going by statement: 4 contestant chosen from 7 -- 7C4 == 35   and total ways =210   Consider 2 supervisor will be chosen from : X people.   So as per question: 35*X= 210   X= 6   So by using options,   Option A already decided wrong.   Option B 2C2 will be 1 not 6.   Option C 3C2 will be 3 not 6   Option D 4C2 will be 6 correct answer   Option E 5C2 will be 10 not 6.   ANS:4
<result>D</result>
For an international Mathematics Olympiad, country D will send six delegates in total — two will be supervisors and four will be contestants. There are 210 ways in which the six delegates can be chosen and there are seven candidates competing for the four contestants’ places available. How many candidates are competing for the two supervisors’ slots available?