A Pune firm must send 4 of its 9 employees to a training programme. Two of the nine, Ravi and Meera, have made it clear they will not go together. In how many ways can the group of 4 be chosen?

All groups: C(9,4) = 126. Groups holding BOTH Ravi and Meera: those two take 2 of the 4 places and the other 2 come from the remaining 7, C(7,2) = 21. Allowed = 126 − 21 = 105. Trap 35 = C(7,4) drops both of them from the pool, but the condition only bans them TOGETHER — either one may go alone. Trap 70 = C(8,4) removes just one person. Trap 126 ignores the condition.