Question

Four officers F1,F2,F3,F4 who arrive late for a dinner party ,find that only one chair at each of five tables T1,T2,T3,T4 and T5 is vacant .F1 will not sit at T1 or T2,F2 will not at T2 ,F3 will not sit at T3 or T4,and F4 will not sit at T4 or T5.Find the number of ways they can occupy the vacant chairs.

Answer 1

Answer:

On the first chair, T1, the no. of people than can sit are 3, namely, F2, F3 and F4.

On the second chair, T2, the no. of people that can sit are 2, namely, F3 and F4.

On the third chair, T3, the no. of people that can sit are 3, namely F1, F2 and F4.

On the fourth chair, T4, the no. of people that can sit are 2, namely, F1 and F2.

On the fifth chair, T5, the no. of people that can sit are 3, namely, F1, F2 and F3.

Now,

Multiplying the no. of ways people can be arranged on each chair = 3 × 2 × 3 × 2 × 3 = 27 × 4 = 108

Hence, people can be arranged in 108 ways on these 5 chairs.

Hope you understood :)