Question

There are 6 boys and 8 girls in a group of students. Calculate the number of ways that a president, vice-president and treasurer can be selected.

Please show your work.

Answer 1

14 students in all, no one student can occupy two posts.

Choose a president from 14 students, a vice-president from 13 remaining students, and a treasurer from the 12 remaining students.
There are six (3!) ways to "shuffle" the three posts, so
for a total of
14*13*12/3! = C(14,3) = 14!/((14-3)!3!)
ways

Answer 2

14 students in all, no one student can occupy two posts.

Choose a president from 14 students, a vice-president from 13 remaining students, and a treasurer from the 12 remaining students.
Number of ways to choose three distinct posts
=14*13*12
=14!/(14-3)!

Answer 3

thank you so much!

Answer 4

You're welcome!