CAT 2006 — QA Question 22
Answer the following question based on the information given below.
An airline has a certain free luggage allowance and charges for excess luggage at a fixed rate per kg. Two passengers, Raja and Praja have 60 kg of luggage between them, and are charged Rs. 1200 and Rs. 2400 respectively for excess luggage. Had the entire luggage belonged to one of them, the excess luggage charge would have been Rs. 5400.
There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to person 2; task 2 must be assigned to either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done?
Answer & solution
144
- B
180
- C
192
- D
360
- E
716
Task 2 can be assigned in 2 ways (either to person 3 or 4).
Task 1 can then be assigned in 3 ways (persons 4 or 3, 5 and 6)
The remaining 4 tasks can be assigned to the remaining 4 persons in 4! = 24 ways
∴ The assignment can be done in 24 × 2 × 3 = 144 ways
Hence, option (a).