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
Answers
Answered by
4
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.
Answered by
1
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
- we have to consider all 7 civil engineers as 1
- So now the total number of engineers will be 12.
- As we grouped 7 civil engineers as 1 , they can be arranged in 7 ways.
- 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!).
Similar questions