Permutation of subsets with like objects Question

[Astro]

Permutations of subsets with like objects Question

Hello, I'd like to know if I solved the question correctly; if not, I'd appreciate some help.

Question:
Calculate the number of permutations for a subset of 3 objects from a superset of 8 objects where 5 are alike.

My solution attempt: (Please see attachment).

 

[Dick]

Your solution is fine except for the factors like C(5,2). This looks like you are counting the ways of picking 2 objects from 5 identical objects. That's not C(5,2). It's 1.

 

[Astro]

Thank you, you're input helped! I believe the answer is 106, not 196. I was going to post a detailed and neat explanation of how I got 196 but I'm so busy that I can't (which is why it took so long for me to reply); however, since I asked for help and you were nice enough try, the least I can do is post my rough work for you and others to see. I'm pretty sure I got it right this time; if not, someone, let me know.