# I want to make sure I did this problem correctly before I add it to the problems section

How many sets of a, b, c, d, e are possible if:
ac + ae + bd + bc + ad + be + 17 = 40
And if a, b, c, d, e are all integers greater than or equal to zero?

So subtracting 17 and factoring yields
(a+b)(c+d+e)=23
since 23 is prime, its only factors are 23 and 1
if a+b=1 then c+d+e=23
and if a+b=23 then c+d+e=1

the first case, a and b can add up to 1 in 2 ways, or 2C1 ways and c d and e can add up to 23 in 25C2 ways or 300 ways.
Therefore, there would be 2*300 or 600 ways for this to happen

the second case, a and b can add up to 23 in 24C1 or 24 ways and c d and e can add up to 1 in 3C1 ways or 3 ways.
Therefore, there would be 24*3 or 72 ways for this to happen

Can someone tell me whether this is done correctly? Thanks,

Note by Dan Huang
3 months, 3 weeks 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:

Yup. Totally correct. Well done!

- 3 months, 2 weeks ago