# Math Help - Probability & Calculus problem

1. ## Probability & Calculus problem

First problem:
''From a company of 12 soldiers, a squad of 4 is chosen each night.
a) For how many nights a squad go on duty without tow of the squads being identical ?
b) In how many of these squads would a particular soldier be included ?''

For a), x=4, n= 12 using Combinatory analysis and found 495

For b) I multiplied C x=4 n=12 by C x=1 n=4 and got 1980

Anyone can confirm my results?

2nd problem:

I'm stuck in this following problem:

'' A publishing company sells 400,000 copies of a certain book each year. Ordering the entire amount printed at the beginning of the year ties up valuable storage space and capital. However, running off the copies in several partial runs throughout the year results in added costs for setting up each printing run. Setting up each production run costs \$1,000. The carrying costs, figured on the average number of books in the storage, are 50 cents per book. Find the economic lot size, that is, the production run size that minimizes the total setting up and carrying costs. ''

My guess was to say that the cost function is: C(x) = 1000 + 0.50(x)

I'm having a hard time even understanding what the problem is all about.

HELP?

2. ## Re: Probability & Calculus problem

First problem, part a seems right. But if the total number of squads is 495, then how can a soldier be in 1980 squads? Seems to high.
On the second problem, the aim seems to be to find the appropriate batch size. The cost will vary with batch size and you want to find a minimum cost. So you should find an equation for cost in terms of batch size and then differentiate to find a minimum point.

3. ## Re: Probability & Calculus problem

Originally Posted by companion2025
First problem:
''From a company of 12 soldiers, a squad of 4 is chosen each night.
a) For how many nights a squad go on duty without tow of the squads being identical ?
b) In how many of these squads would a particular soldier be included ?''
$\binom{12}{4}$

If $\mathcal{T}$ is one of those $N$ individuals it can be in $\binom{N-1}{j-1}$ cells.

So what is the answer to b)?

4. ## Re: Probability & Calculus problem

a) 495
b) 495 - 330 = 165

5. ## Re: Probability & Calculus problem

Let c = cost of books, r = runs, b = batch size

$c=1000r+0.5b$

But $r=\frac{400,000}{b}$

So $c=\frac{400,000,000}{b}+0.5b$

Now differentiate with respect to b and find a minimum.