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.
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