Question

A Company has 11 software engineers and 7 civil engineers. In how many ways can they be seated in a row so that civil engineers do not sit together​

Answer 1

Answer:

Total number of engineers =11+7=18. Now we will find out the total number of ways in which these 18 engineers can be arranged so that all the 7 civil engineers will always sit together. For this, group all the 7 civil engineers and consider as a single civil engineer. Hence, we can take total number of engineers as 12.

Answer 2

Number of ways they be seated in a row so that civil engineers do not sit together

18!-(12! * 7!)

Given

11 software engineers

7 civil engineers

And hence

Total engineers are 11 + 7 = 18

• Since there are 18 engineers they can be seated in a row in 18 different ways.

___________(A)

• And now to find out In how many ways can they be seated in a row so that civil engineers do not sit together

1. we have to consider all 7 civil engineers as 1
2. So now the total number of engineers will be 12.
3. As we grouped 7 civil engineers as 1 , they can be arranged in 7 ways.
4. So the total number of ways 18 engineers can be arranged will be

= 12! * 7!.

___________(B)

Therefore from (A) and (B)

the total number of ways that they can be seated in a row so that civil engineers do not sit together

is 18!-(12! * 7!).