I think part 1 is wrong. It should be
7! / ( 3! x 2! x 2! )
For explanation, refer to this link 3. Permutations (Ordered Arrangements)
1. In how many ways can 3 identical emeralds, 2 identical diamonds, and 2 different opals be arranged in a row in a display case?
Is the solution 3 x 2 x 2 =12
2.Find the number of 6-letter permutations that can be formed from the letters i n the world shopper.
C (7,6) =7
3. How many 13-card hands having exactly 10 spades can be dealt?
Thank you very much.