Question

Three children, each accompanied by a guardian, seek admission in a school. The principal wants to interview all the $6$ persons one after the other subject to the condition that no child is interviewed before its guardian. In how many ways can this be done?

• A. $60$
• B. $90$
• C. $120$
• D. $180$

Answer 1

The correct option is B $90$

Since no child is interviewed before the guardian, we consider ordered pairs of guardian-child while solving . Since there are six places and we fill up 2 in an order we get the total number of possibilities as ${}^6{C}_2{\times }^4{C}_2{\times }^2{C}_2$ = 90