How many ways can 5 days are chosen from each of 12 months of an ordinary year of 365 days.

Question

How many ways can 5 days are chosen from each of 12 months of an ordinary year of 365 days. Here my doubt is, how should I solve the problem:

1) 31c5+28c5+31c5+....+30c5 (or)
2) 31c5*28c5*31c5*....*30c5 (or)
3) 31p5+28p5+31p5+....+30p5 (or)
4) 31p5*28p5*31p5*....*30p5 (or)
5) 365c5 (or)
6) 365p5

Please tell me how to solve these kind of questions. And also someone please explain where should I use C(combination),P(Permutation),where should I use +(sum) and where to use *(product).

Can anyone explain clearly to me because most in internet is not in clearly understanding way.Please let me understand where to use which?

Thanks in Advance.

Answer 1

$${31 \choose 5}{28 \choose 5}{31 \choose 5}{30 \choose 5}{31 \choose 5}{30 \choose 5}{31 \choose 5}{31 \choose 5}{30 \choose 5}{31 \choose 5}{30 \choose 5}{31 \choose 5}$$

$$= {31 \choose 5}^7 {30 \choose 5}^4 {28 \choose 5} $$

$$= 165709809987064484293093112435985007113574028261399196848004480$$