Discrete Math

1)

a) Suppose you have a random string of 6 bits. What is the probability that the string has exactly 3 0's? Give your probability as a decimal, not a percentage. Give your answer to two decimal places.

b) Suppose 7 customers at a restaurant ordered an appetizer, 6 customers ordered a main dish, and 5 customers ordered an appetizer and a main dish. How many customers ordered an appetizer or a main dish?

c) A group of 9 people are attending the movies together. Two of the 9 insist on not sitting next to each other. In how many ways can the eight be seated together in a row?

d) A tasting menu has 13 different items. How many ways can you pick 4 items to try?

e) Suppose a certain combination lock requires three selections of numbers, each from 0 through 26. How many combinations are possible?

f) Suppose a certain combination lock requires three selections of numbers, each from 0 through 21. Suppose the lock is constructed so that no number may be used twice. How many combinations are possible?

g) You have 3 red plates, 3 green plates, and 4 blue plates. How many distinguishable ways can you stack the plates?

h) Suppose a certain combination lock requires three selections of numbers, each from 0 through 30. What is the probability that a randomly selected combination has a repeated number? Give your answer as a decimal probability, not a percentage. Give your answer to exactly two decimal points.

i) How many integers from 1 through 81 must you pick in order to be sure of getting one that is divisible by 5?

j) How many integers from 1 through 82 must you pick in order to be sure of getting at least two of them that have the same remainder when divided by 4?

k) A group of 7 people are sitting in a circle at the park for a picnic. Two seatings are considered the same if one is a rotation of the other. How many different seatings are possible?