Question

A committee of 4 persons is to be chosen from 8 persons including Mr.Smith and his wife. Mr.Smith will not join without his wife but Mrs.Smith would join without Mr. Smith. Calculate the number of possible ways the commitee can be formed.

Answer 1

if the positions are not unique, then
assuming both join, 6C2 (since only 2 positions have to be filled from the 6 remaining candidates)
assuming only she joins, 6C3 (3 positions have to be filled from the remaining 6 candidates)
now add the two cases