Optional problems with solution
Problem 4.1 In how many ways can you
- draw a first card and then a second card from a 52-card deck?
- draw a two cards from a 52-card deck?
- draw a first, second, and third card from a 52-card deck?
Give reasons for your answers?
Problem 4.2 (Video Solution «Counting dinners») A dinner meal ought to comprise both starch and protein. Suppose you have the options of potatoes, rice, and spaghetti for the starch and beef, chicken, or meatballs for the protein.
How many different dinners can you cook? Assume that you are allowed only one ingredient of each type.
Problem 4.3 You take part in an urban orienteering race, where you have to visit three out of five posts in any order. The posts are, say, Fjellstuen, the church at Aspøya, Kremmergården, Gågaten, and Byparken.
How many iteneraries are possible.
Problem 4.4 (Paraphrased from Stein et al. Section 1.2) A password (for some computer system) is between four and eight characters long (inclusive), and composed of lowercase and/or uppercase letters (26-letter alphabet).
- How many passwords are possible?
- What counting principle(s) do you use?
- What percentage of valid passwords have exactly four letters?
Problem 4.5 A basketball team has twelve players, with five players on the field at any time.
- In how many ways can the coach choose the five players?
- In how many ways can the coach choose the
players, given that he has five guards, four forwards, and thre centres on the team?
- Suppose one of the three centres is also skilled as a forward. How many ways are there to choose the five players now?
Problem 4.6 (Video Solution «Lotto») What is the probability of getting 7 correct numbers in a lotto ticket (playing one row only)?
The draw selects 7 random numbers out of a pool of 34 numbers. You need to start by calculating the number of possible 7-sets that can be drawn.