Combinations Exercises

When doing data analysis it happens often that we have a set of values and want to obtain various possible combinations of them. For example, taking 5 random samples from a dataset of 20. How many possible 5-sample sets are there and how to obtain all of them? R has a bunch of functions that help with tasks like these: expand.grid, combn, outer and choose.

Answers to the exercises are available here.

If you obtained a different (correct) answer than those listed on the solutions page, please feel free to post your answer as a comment on that page.

Exercise 1
You first throw a coin with 2 possible outcomes: it either lands heads or tails. Then you throw a dice with 6 possible outcomes: 1,2,3,4,5 and 6.
Generate all possible results of your action.

Exercise 2
Generate a multiplication table for numbers ranging from 1 to 10.

Exercise 3
You have a set of card values:
values <- c("A", 2, 3, 4, 5, 6, 7, 8, 9, 10, "J", "Q", "K")
and a set of suits representing diamonds, clubs, spades and hearths:
suits <- c("d", "c", "s", "h")
Generate a deck of playing cards. (e.g. King of spades should be represented as Ks).

Note: function paste(..., sep="") can be used to combine characters.

Exercise 4
Think about a game of poker using a standard deck of cards like the one generated earlier. Starting hand in poker consists of 5 cards and their order does not matter. How many different starting hands are there in total?

Exercise 5
You have a set of colors to choose from:
colors <- c("red", "blue", "green", "white", "black", "yellow")
You have to pick 3 colors and you cant’ pick the same color more than once. List all possible combinations.

Exercise 6
Using the same set of colors – pick 3 without picking the same more than once, just like in the previous exercise.
List all possible combinations but this time sort each combination alphabetically.

Exercise 7
You have the same choices of colors and have to pick 3 but this time you can pick the same color more than once.
List all possible combinations.

Exercise 8
You have the same set of colors but this time instead of having to pick 3 you can choose to pick either 1, 2 or 3.
How many different choices can you make?

Exercise 9
You have the same set of colors and you can choose to pick either 1, 2 or 3.
Make a list of all possible choices.

Exercise 10
There are 3 color palletes: the first one has 4 colors, the second has 6 colors and the third has 8 colors. You have to pick a pallete and then choose up to 5 (1, 2, 3, 4 or 5) colors from the chosen color pallete. How many different possibilities are there?