Math 128 Test 1

How many distinguishable passwords can be written using all of the letters in the word statistics s-3 t-3 a-1 i-2 c-1 ----- 10

10! 3628800 ---- = ------------- = 3! 3! 2! 6 x 6 x 2 3628800 --------- =50,400passwords 72

You need a six-digit password that starts with 4 letters and ends with two numbers. A) In how many ways can you form the password if repeats are allowed? B) In how many ways can you form the password if repeats are not allowed?

26 26 26 26 10 10 ----x---x----x---x---x---- = A-Z 0-9 45,697,600 ways B) 26 x 25 x24 x23 x10 x9 = ---------------------------- A-Z 32,292,000 ways

A multiple choice test has 5 questions and each question has 4 answer choices. If you don't leave any questions blank, in how many ways can you answer the questions?

4 x 4 x 4 x 4 x 4 = 4^5 = 1024 ways

A restaurant offers 6 appetizers, 5 entrees and 3 desserts. In how many ways can you order 1 appetizer and 1 dessert?

6 x 3 = 18 ways app desserts

In how many ways can a club elect a president, a vice president, a treasure and a secretary from its 75 members? no repeats order matters permutation

75 P 4 = 29,170,800 ways

In how many ways can a host choose a catered dinner if he/she is going to choose 3 different entrees from the available and 5 different side dishes from the 11 available? no repeats order doesn't matter combinations

8C3 x 11C5 = 56x462 = entr sides 25,872 ways

Given the following options: M, N, P, and Q a) List all 3-item combinations no repeats order doesn't matter b) List all 2-item permutations no repeats order matters

a) MNP MNQ MPQ NPQ b) MN NM PM QM MP NP PN QN MQ NQ PQ QP