Question

Suppose that we have seven rooms and want to assign four of them to four programmers as offices and use the remaining three rooms for computer terminals. In how many ways the assignment can be made (Assuming that programmers are distinct but that all computer terminals are identical)?

Answer 1

To solve this problem, we can use the concept of combinations. We need to choose 4 rooms out of 7 for the programmers' offices, and the remaining 3 rooms will be used for computer terminals.

The number of ways to choose 4 rooms out of 7 for the programmers' offices is given by the combination formula:

(7 4)=7!/4!(7−4)!=7!/4!3!=7×6×5/3×2×1=35(47​)=4!(7−4)!7!​=4!3!7!​=3×2×17×6×5​=35

This represents the number of ways to choose which rooms will be assigned to the programmers' offices.

Since the computer terminals are identical, once we have chosen the rooms for the programmers, the assignment of the remaining rooms to the computer terminals is fixed.

So, there are 35 ways to make the assignment.