Let's say I have the following 10 distinct items: {a,b,c,d,e,f,g,h,i,j}.
How many combinations are there if I can choose UP TO 10 items and order does not matter and items cannot be repeated?
I'm thinking that it is simply the sum of all the C(n,r)s, correct?
r0 = 1
r1 = 10
r2 = 45
r3 = 120
r4 = 210
r5 = 252
r6 = 210
r7 = 120
r8 = 45
r9 = 10
r10 = 1
Thus, 1024 combinations???
I appreciate any help… These always trip me up!
Best Answer
That’s correct. It’s equivalent to asking how many subsets of a set with $m$ elements are possible with size no more than $n$. We can either choose $0$ elements, or $1$ element, or $2$, or $3$ and so on till $n$ elements. The answer would be then be $$\sum_{i=0}^n {m \choose i}$$