Probability question...

23:38 Publicado por Mario Galarza

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

These are the answers:

d) 420
e) 672
f) 540

This is what I did:

d) if only one Smith must be included, then the other Smith is not a part of "n" anymore...therefore I said,

$\displaystyle \binom{11}{7}$

Then, considering the other Smith...since he MUST be chosen, I subtracted 1 from both 11 and 7...because if he is chosen, then only 6 others need to be chosen, and n=10...since Smith is gone...so...

$\displaystyle \binom{10}{6}$ = 210...obviously, my answer is wrong, but I can't understand why.

e) Considering that one Smith MUST be chosen, I subtracted 1 from 12 and 7...I did not consider the other Smith, since it does not matter whether he is chosen or not.

$\displaystyle \binom{11}{6}$ = 462...which is also wrong