6. In how many ways can a president, a treasurer, and a secretary be chosen from among nine candidates if no person can hold more than one position?

Answer: 84ways

Step-by-step explanation:

Since we are selecting 3candidates (president, a treasurer, and a secretary) from a pool of 9 candidates if no person can hold more than one position, that will be 9C3

Note that combination has to do with selection. Generally if 'r' candidates are selected from pool of 'n' candidates, this can be done nCr ways.

nCr = n! / (n-r) ! r!

9C3 = 9! / (9-3) !3!

9C3 = 9!/6!3!

9C3 = 9*8*7*6!/6!3!

9C3 = 9*8*7/3*2

9C3 = 84ways

The 3 candidates can be selected in 84ways.