The number of words you can find within the phrase "sports center" depends on the rules you set for word formation. If you allow any combination of letters that form valid English words, you can find quite a few. Here are some examples:

1. Sport
2. Sports
3. Center
4. Cent
5. Ten
6. Sent
7. Rent
8. Port
9. Ports
10. Sort
11. Sore
12. Rose
13. Rest
14. Core
15. Tore
16. Rots
17. Rote
18. Stern
19. Spore
20. Stone
21. Note
22. Ton
23. Net
24. Pet
25. Pen
26. Cot
27. Con
28. Nor
29. Son
30. Set

This is not an exhaustive list, but it gives you an idea of the variety of words you can form. The total number will vary based on the length of words you consider and whether you allow proper nouns, abbreviations, or less common words.