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## 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?

## Homework Equations

## 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}

b)E={head}

c)F={heads>tails}

d)E U F ={head,tail}

e)E n F

f)(E U F)

^{c}= {tails>heads} ? isnt it the De Morgan's where E

^{c}F = (E U F)

^{c}?

g)= {tails>heads}

h) impossible? like logic's (0 and 1) and 1 = 0?

Thank you !