Question

In how many ways can 5 men be seated in a row so that 2 particular men will not will not be next to each other

Answer 1

Total number of ways 5 men can be seated =5P5=5.4.3.2.1=120=5P5=5.4.3.2.1=120

Now let us find the total number of ways when two particular men will be seated next to the other

For this we need to take the two particular men as one. This gives us 44P44=4.3.2.1==4.3.2.1= 2424ways. Also the two men can be seated between themselves in 2P2=22P2=2ways. So in total there are 24.2=48 ways.

Therefore total number of ways when two particular men will not be seated next to each other =120−48=72.=120−48=72.

Hope you got it.

Answer 2

Answer:

Total number of ways that two particular men will not be seated next to each other = 72