R Bridge Week 2 Assignment

Logan Thomson

The choose() Function

R has a built-in function for combinations, which is a formula for the number of combinations possible from a given set. This can be written out several ways, it is commonly seen as

\(_nC_r\)

The Combination Formula

To calculate the number of ways n items can be chosen in sets of r, we make use of the factorial:

\(\frac{n!}{r!(n-r)!}\)

Writing our own combination function

R has built-in functions for both the combination formula (see above), and the factorial. Following is how you can calculate a combination without using either built-in function:

Calculating the factorial

First, we need to create the factorial function. I have done this using a for loop.

my_factorial <- function(t){
  x <- 1
  for (i in 1:t){
    (x<- x * i)
  } 
  return(x)
} 

Let’s test the function and see the returned calculation:

my_factorial(5)

## [1] 120

Creating the combination function

Now that we have a working factorial function, we can simply enter this into the combination formula to calculate the possible combinations from a given set of objects:

my.combo <- function(n, r){
  combo <- (my_factorial(n) / (my_factorial(r) * my_factorial(n - r)))
  return(combo)
}

my.combo(6, 2)

## [1] 15

my.combo(5, 3)

## [1] 10

Looks like we have success!