# Stars and Bars with Restriction

I just encountered the stars and bars technique page on Brilliant. https://brilliant.org/assessment/techniques-trainer/stars-and-bars/

The example problem asks How many ordered sets of non-negative integers are there such that $$a + b + c + d = 10$$

I was wondering, If an upper limit is placed on one or two of the variables, for example if $$a<5$$ and $$b<4$$, then how will the solution change?

Note by Sameer Jain
4 years, 10 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

Okay brother the solution is simple First find the no of solutions without any restriction Now you have to subtract 3 cases, Case 1 When a =5 then the solve b+c+d=5; Case 2 When b=4; Case 3 When both a and b are at their maximas.; Subtract these cases from your solution. PS- case 3 is not valid in this case.

- 4 years, 7 months ago