在 R 循环中的 choose(k, n) 中查找组合

Question

I need to find the SUM of all possible combinations in a set. For example:

sum(choose(5, 0),

    choose(5, 1),

    choose(5, 2),

    choose(5, 3),

    choose(5, 4),

    choose(5, 5))

Instead of writing it out like that, is possible to use a for loop to loop through choose() with any given n and k ?

Answer 1

You can use

> sum(choose(5, 0:5))
[1] 32

or just apply the binomial sums

> 2^5
[1] 32

Answer 2

In case you want to do this for more than just one n you can use sapply

setNames( sapply( 1:10, function(x) sum( choose( x, 0:x ) ) ), 1:10 )
   1    2    3    4    5    6    7    8    9   10 
   2    4    8   16   32   64  128  256  512 1024