Permutations and Combinations with Probability

Choosing 3 toppings for your sundae out of a list of 15. (a)  

• Permutation

• Combination

Picking a President, Vice-President, and Secretary from a group of 12. (a)  

• Permutation

• Combination

Calculate:

₁₂P₄

• 24

• 132

• 1320

• 11880

There are 12 kinds of Girl Scout cookies for sale. How many ways can Rachel choose three different kinds to buy?

• 220

• 36

• 1320

• 100

Student council has 24 members.  In how many different ways can a president, vice-president, treasurer, historian, and secretary be selected?  

• 5,100,480

• 0

• 42,504

• 5.17 x 10²¹

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

Simplify the expressions 6P5

• 1

• 30

• 720

• 6

Calculate the following:

₁₂P₅

Mathematical Equivalence

ON

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

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?