a company has 11 engineers 7 civil engineers . how many way can they seated in a row so that no two of the civil engineer will seat together.
a) qq! . ¹¹p7. b) 7! . ¹¹p7. c) 11! . ¹²p7. d) 12! . ¹¹p7
Answers
Answer:
64. A company has 11 software engineers and 7 civil engineers. In how many ways can they be seated in a row so that all the civil engineers do not sit together?
A. 18P4 × 11 B. 18! - (12! × 7!)
C. 18P4 - 2! D. 18! - (11! × 7!)
Answer: Option B
Explanation:
Total number of engineers
=
11
+
7
=
18
.
These 18 engineers can be arranged in a row in
18
!
ways. ...(A)
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. These 12 engineers can be arranged in
12
!
ways.
We had grouped 7 civil engineers. These 7 civil engineers can be arranged among themselves in
7
!
ways.
Hence, total number of ways in which the 18 engineers can be arranged so that the 7 civil engineers will always sit together
=
12
!
×
7
!
⋯
(B)
From (A) and (B),
Total number of ways in which 11 software engineers and 7 civil engineers can be seated in a row so that all the civil engineers do not sit together
=
18
!
−
(
12
!
×
7
!
)