# Basic Combinatorics

## Homework Statement

Here is some basic combinatorics, I need someone to check it for me, please before the lecturer :)
Sorry for the stupid questions, hope i've made myself clear with the explanations of the answers given.

(1)(a) If 8 cooks are to be divided among 4 restaurants, how many divisions are possible?
(b) What if each restaurant must receive precisely 2 cooks?
(c) How many possible ways we can pair these 8 cooks up among themselves?
(d) How many possible ways we can distribute 8 identical bowls into the 4 restaurants?

## The Attempt at a Solution

a) is it 4^8?

b) for the first restaurant we have (8 2) and for the next 3 we have to decrease 2 cooks so we have (8 2) * (6 2) * (4 2) * (2 1)

c) 8! ?

d) V 4 8 = 1680?

2
a) S = {E,F}
e)E n F
f)(E U F)c = {tails>heads} ? isnt it the De Morgan's where EcF = (E U F)c?
h) impossible? like logic's (0 and 1) and 1 = 0?

Thank you !

.Scott
Homework Helper
Your answers to 1a and 1b are correct - assuming that it is okay for a restaurant to have no cooks.
1c is the same as 1b - because I doubt that they mean to make copies of the cooks.
I'm getting 165 for 1d.

Office_Shredder
Staff Emeritus
Gold Member
2021 Award
1c is not the same as 1b, because once you've paired up the cooks there are a couple different ways you can put each pair in a restaurant (and that should be enough to figure out what the correct solution is).

haruspex