Question

If 11 books are kept in 4 shelves then there must be at least one shelf which contain at least three books pigeonhole

Answer 1

Answer:

a) 25P25 for the first place, as order matters and there's 25 ways the books could be arranged on that shelf, or it could be in the second place, third, etc. so (25P25)∗10?

Or would I do it like a Stars and Bars question? Because the above answer is massive.

b) Order doesn't matter, so combinations now. Would I do 25C25∗10? Or is there a way to differentiate Stars and Bars between permutations and combinations?

c) Stars and Bars but with the restriction of each gap having one at least?

Step-by-step explanation:

Answer 2

Answer: n=11 , K + 1 = 4 i.e K = 3

=> Kn+1 = 11*3 + 1 =34

Step-by-step explanation:

in this question, we will use generalise pigeon-hole formula which is

if n pigeon-hole is occupied by Kn+1 or more pigeons then at least one pigeonhole is occupied by K+1 on more Pigeons.