Counting

Question

I am solving with Pigeon Hole Principle. Please correct me if I am wrong.

Considering the required number of books as pigeons, days of the month as pigeonholes with 3 pigeons per day.

if my approach is wrong, please correct me

Comments

I think no of holes are poems in set of 3 ,k+1=3 ,k=2 And assuming no of days in month as 30,kn+1=61 poems are necessary

---

will it be 61?

---

month can be of 30 or 31 days , 7 poems can keep her busy for 35 days :P

to create different sets of 3 we need to choose 3 poems out of 7 poems

⁷C_{3 =} 35

---

@Mk Utkarsh,

Can you please explain this statement?

7 poems can keep her busy for 35 days :P

---

the book contain 7 distinct poems and she needs distinct set of 3 poems every day

to choose 1st poem she has 7 options

to choose 2nd poem she has 6 options

to choose 3rd poem she has 5 options

but these are permutations so we need to divide by 3! because we don't care about the order.

$\frac{7 * 6 * 5}{3 * 2}$ = 35

that means we have 35 distinct set of 3 poems from 7 distinct poems