Practising NCR in Combinations in Probability

A group of 40 people are going to run a race.  The top 6 finishers advance to the finals. How many different outcomes can happen?

• 2866425

• 1919190

• 3838380

• 2568929

₁₅C₂

• 15

• 105

• 455

• 1365

Find the possibilities when a group of 15 people are going to run a race.  The top 5 finishers advance to the finals.

• 3 x 10¹²

• 120

• 3003

• 360,360

How many ways can 8 cheerleaders be chosen for 3 positions on the cheer team?

• 24

• 56

• 128

• 336

₁₂C₃

• 0

• 1

• 220

• 1140

Which is greater, ₈C₃ or ₈C₅?

• ₈C₃ = ₈C₅

• ₈C₃ > ₈C₅

• ₈C₃ < ₈C₅

Which of the following is an example of combination?

• Form a passcode with 4 digits

• Students line up in a queue to assembly

• Choose 4 students in a class committee

• Choose the chairperson, secretary and treasurer in a club

4 out of 19 students will ride in a car instead of a van. How many different outcomes can happen?

• 7752

• 3876

• 15504

• 93024

The student body of 35 students wants to elect three representatives. How many different outcomes can happen?

• 6545

• 13090

• 39270

• 19635

What is the formula for Combinations?

• ^n!∕_(n-r)! r!

• ^n!∕_(n-r)!

• ^r!∕_{(r-n)! n!}

• n!