Representatives from four different colleges of UM Dearborn

Representatives from four different colleges of UM- Dearborn will be seated in a row. There are 4 representatives from College of \'Art Sciences, and Letter\', 3 from college of \'Business\', 5 from College of \'Education, Health and Human Services\', and 6 from \'College of Engineering and Computer Science\'. Representatives will be seated according to their colleges (identities of each representative is not important). In how many different ways will these representatives be seated?

Solution

4 from college of \'arts sciences and letter\' arranged in 4! ways =24 ways

3 from college of \'business\' arranged in 3! ways = 6 ways

5 from college of \'education health and human sevices\' arranged in 5! ways = 120 ways

6 from college of \'engineering and computer science\' arranged in 6! ways = 720 ways

  

And these four college can be arranged in 4! ways i.e., 24 ways

So total = 24*24*6*120*720 = 298598400 ways