Expansion of (a+b)n using binomial coefficients, including the general term (nr)an−rbr
If we have n ways to do one thing and k to do another, then there are n×k ways to do BOTH (first thing AND the second thing), and n+k ways to do one thing OR the other thing.
In any scenario where we can put k items into each of n positions, we have kn possible arrangements.
The number of different orders in which n items can be arranged is
where each box is a "slot" in the order. In the first slot we can put any of n items, in the second any of the n−1 remaining items, and so on. We then multiply all of these together to get n!
The number of permutations, defined as an ordered arrangement, of r items from a set of n items can be calculated by:
Combinations are arrangements of items where order does not matter. For combinations of r items from a set of n:
which is the binomial coefficient.
Nice work completing Counting, here's a quick recap of what we covered:
Exercises checked off
Expansion of (a+b)n using binomial coefficients, including the general term (nr)an−rbr
If we have n ways to do one thing and k to do another, then there are n×k ways to do BOTH (first thing AND the second thing), and n+k ways to do one thing OR the other thing.
In any scenario where we can put k items into each of n positions, we have kn possible arrangements.
The number of different orders in which n items can be arranged is
where each box is a "slot" in the order. In the first slot we can put any of n items, in the second any of the n−1 remaining items, and so on. We then multiply all of these together to get n!
The number of permutations, defined as an ordered arrangement, of r items from a set of n items can be calculated by:
Combinations are arrangements of items where order does not matter. For combinations of r items from a set of n:
which is the binomial coefficient.
Nice work completing Counting, here's a quick recap of what we covered:
Exercises checked off