Question

There are 9 students running for 4 openings on the student council. Only students who are running for election can be elected; no write-in candidates are allowed. An elected student can only hold one position at a time. Use Pascal’s Triangle to find the number of different ways 4 students can be elected from the group of 9 candidates.

Answer 1

9 students, 4 are selected and order doesn't matter:

Go to the 9th row of the triangle (mind you the first row is 0), the 2nd is 1st row

9th row: 1   9   36   84   126   126   84   36   9   1
Now choose the 4th column (excluding the 1st , you will get 126 :
 so 126 is the number of combination requested:

PROOF: ⁹C₄ = 9!/(9-4)! .4! = (9!)/5!.4! = 126