How many ways can you choose up to three items form 7

[wind]

Hi can someone tell me what I'm doing wrong?

How many ways can you choose up to three items form a set of 7 different items?

I thought

0 items 7C0
1 item 7C1
2 items 7C2
3 items 7C3

7C0+7C1+7C2+7C3=64


but the answer is 35 which would be 7C3....

Thanks

 

[pka]

You are correct; the answer key is not!