Combinations 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

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

Ambry must submit 4 paintings as part of her
application to art school. If she has 25 to choose from, how many ways can she pick 4?

• 12,650

• 303,600

• 100

• 254

Ten students in your math class are presenting unique proofs to their classmates.  The order in which the proofs are chosen to be presented is random.   Find the probability that the proof using the HL Theorem is chosen first and your proof on CPCTC Theorem is chosen to go second.  

• 1/10

• 1/10!

• 4/5

• 1/90

Permutation or Combination?

There are eight seniors on the football team that are being considered as team captains.

If there will be 3 team captains, how many different ways can 3 of these seniors be

chosen as captains?

• Permutation

• Combination

The Nebraska license plate has 6 characters, each one filled with a number (0-9) or a letter. How many license plates are possible?

• 36

• 2176782336

• 60

• 1402410240

How many ways can 8 runners finish in the top 3 places where the prizes for 1^st, 2^nd, and 3^rd are all different and matter?

Mathematical Equivalence

ON

What would plug into your calculator for the following scenario: There are 10 people running for treasurer and vice-president. How many different arrangements could you have?

At Wafer Technologies, identification codes each consist of the following sequence: 1 digit, 4 letters, 1 digit. For any 1 code, the digits (0-9) may be the same but he letters, each from the English alphabet, must all be different. Which of the following expressions gives the probability that a randomly selected identification code contains the word MATH, spelled correctly?

₁₂C₃

• 0

• 1

• 220

• 1140