Given that:
- Ralph hosts one guest per day
- The show runs for Mondays to Fridays (5 days)
- Politicians are scheduled for Mondays and Wednesdays (2 days)
- Actors come up on Tuesdays (1 day)
- Athletes come up on Thursday (1 day)
- Any of politician, actor or athlete can come up on Friday
- No guest appears more than once per week
- Ralph has 5 politicians, 3 actors, and 6 athletes

=> How many different schedules of guests from Monday to Friday could Burke create?

$$5\ politicians\ can\ be\ selected\ on\ Mondays\ and\ Wednesdays$$
$$in\ 5C1=\frac{5!}{1!\left(5-1\right)!}=5\ ways\ on\ monday$$
$$in\ 4C1=\frac{4!}{1!\left(4-1\right)!}=4\ ways\ on\ wednesday$$
$$-\ 3\ actors\ can\ be\ selected\ on\ tuesday\ in;$$
$$3C1=\frac{3!}{1!\left(3-1\right)!}=3\ ways\ on\ tuesday$$
$$-\ 6\ athletes\ on\ thursday\ can\ be\ selected\ in;$$
$$6C1=\frac{6!}{1!\left(6-1\right)!}=6\ ways\ on\ thursday$$


If guests have been selected between Monday and Thursday, the remaining guests to select from = 5 + 3 + 6 - 4 = 10
$$10C1=\frac{10!}{1!\left(10-1\right)!}=10\ ways$$
Total number of possible schedules that can be created = 5 * 4 * 3 * 6 * 10 = 3600

Answer = C