Final answer:
To determine the number of ways to form a committee of 4 engineers with exactly 1 civil engineer out of 10 software engineers and 6 civil engineers, we use the combination formula to calculate that there are 720 ways to form such a committee.
Step-by-step explanation:
The student is asking about combinatorial mathematics specifically related to forming a committee from a group of engineers with a constraint on the composition of the committee. The task is to calculate the number of ways to form a committee of 4 engineers that includes exactly 1 civil engineer from a group of 10 software engineers and 6 civil engineers.
To solve this problem, we will use the combination formula to select 1 civil engineer out of 6 and 3 software engineers out of 10. The formula for a combination is given as C(n, k) = n! / (k!(n - k)!), where n is the total number of items, k is the number of items to choose, and '!' denotes factorial.
The number of ways to choose 1 civil engineer is C(6, 1) = 6!/1!(6-1)! = 6. The number of ways to choose 3 software engineers is C(10, 3) = 10!/3!(10-3)! = 120. Now, to find the total number of ways to form the committee, we multiply these two results together:
Total ways = C(6, 1) x C(10, 3) = 6 x 120 = 720 ways.