sir in the last question ,we know that at least 1 doctor is selected by 2^8 – 1 ways and since only 7 doctors are remaining so shouldn’t it be ( 2^8 – (1+7C1) ways ?
Why do you feel seven are remaining? The two cases are separate. When we say none is selected, we mean none of the 8 (i.e. 8C0). When we say exactly 1, it also means 1 out of the 8 (i.e. 8C1). In this case, we want “at least 2” which means we need to remove the cases of “none” and “exactly 1” from all the 8 available. Which is what we have done here.
Sir, the case where atleast one doctor is selected, if we selected A, corresponding to it, we’ll have 2’7 cases. So, won’t the answer to it be 2’7 for atleast one doc being selected? I see one flaw with this reasoning of mine, that for exactly one doc being selected we’ll have 8 such cases while this 2’7 yields only one, that of only A, whereas it could be B,C and so on, so where am I actually going wrong, Sir?
2^ l be the answer for “one specific doc (i.e. A) being selected”. The question isn’t that, it is just that there should be at least one doc, any one (or more than one) will do.
CAT-holics 
sir in the last question ,we know that at least 1 doctor is selected by 2^8 – 1 ways and since only 7 doctors are remaining so shouldn’t it be ( 2^8 – (1+7C1) ways ?
Why do you feel seven are remaining? The two cases are separate. When we say none is selected, we mean none of the 8 (i.e. 8C0). When we say exactly 1, it also means 1 out of the 8 (i.e. 8C1). In this case, we want “at least 2” which means we need to remove the cases of “none” and “exactly 1” from all the 8 available. Which is what we have done here.
regards
J
nice
Sir, the case where atleast one doctor is selected, if we selected A, corresponding to it, we’ll have 2’7 cases. So, won’t the answer to it be 2’7 for atleast one doc being selected? I see one flaw with this reasoning of mine, that for exactly one doc being selected we’ll have 8 such cases while this 2’7 yields only one, that of only A, whereas it could be B,C and so on, so where am I actually going wrong, Sir?
2^ l be the answer for “one specific doc (i.e. A) being selected”. The question isn’t that, it is just that there should be at least one doc, any one (or more than one) will do.
regards
J