Out of 12 men, just two are named Smith. In how many ways, disregarding the order of selection, can seven of the men be chosen: e) if at least 1 smith must be included? f) if no more than one Smith may be included?

Question

anonymous · Answer

i have ans but still don't understand it well. http://answers.yahoo.com/question/index?qid=20110920184238AAlqUa6

anonymous · Answer

e) 10C5 * 2C2+ 10C6 * 2C1
f) 10C7 + 10C6 * 2C1
This answer is correct. I'll explain why
e) we first the 10 non-Smith people and choose 5 people out of them and multiply it with  2C2 which means "Out of the 2 Smiths we choose 2 Smiths". 
Added to that is the case when only 1 Smith is chosen. So out of the 10 non-Smiths we choose 6 people and multiply it with 2C1 which is - Out of the 2 Smiths we choose 1 Smith.
f) If NO smith is chosen, this means out of the 12 non-Smiths we choose all 7 people (10C7) and add to that the case when ONE Smith is chosen, which is 10C6 * 2C1

Did you get it ?