A committee of 15 members sits around a table. In how many ways can they be seated if the President and Vice-president never sit together ?
A committee of 15 members sits around a table. In how many ways can they be seated if the President and Vice-president never sit together ?
There are 15 members.
The total number of ways in which they can be seated = 15!
The number of ways in which president and vice president do not sit together = 15! – (number of ways in which they sit together).
Since, president and vice-president will sit together. So, they can sit together in 2! ways or 2 × 1 = 2 ways
Now, the position of remaining persons (15 – 2 = 13) will be changed around the table.
So, they can be seated in 13! ways.
Hence, the required number of arrangements = 2! × 13! = 2 × 6227020800 = 12454041600
The number of ways in which president and vice president do not sit together = 15! - 12454041600.
There are 15 members.
The total number of ways in which they can be seated = 15!
The number of ways in which president and vice president do not sit together = 15! – (number of ways in which they sit together).
Since, president and vice-president will sit together. So, they can sit together in 2! ways or 2 × 1 = 2 ways
Now, the position of remaining persons (15 – 2 = 13) will be changed around the table.
So, they can be seated in 13! ways.
Hence, the required number of arrangements = 2! × 13! = 2 × 6227020800 = 12454041600
The number of ways in which president and vice president do not sit together = 15! - 12454041600.
