# Distribution doubt

Angela has to distribute 15 chocolates among 5 of her children cupcake, pancake, lollipop, pie and gingerbread. She needs to make sure that cupcake get at least 3 and at most 6 chocolates. Find the number of ways can this be done. The answer is 435

Okay now I am getting 425. this is my way.
The question is same as asking the number of integer solutions of the equation
$$15=a+b+c+d+e$$ constraint to the relation that $$3\leq a \leq 6$$ and $$1\leq b,c,d,e\leq15$$. Which is equivalent to finding the coefficient of $$x^{15}$$ in $$(x^3+x^4+x^5+x^6)(x+x^2 + \cdots+x^{15})^4$$.

I checked from wolfram alpha that the coefficient is coming out to be 425. But the answer is 435. Can anyone provide a correct solution and tell me what I am doing wrong?

Note by Rishi Sharma
1 year, 7 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:

You're not doing anything wrong. A brute force check using Python also reports that the answer is indeed 425.

- 1 year, 7 months ago

Thanks. Then I guess there must have been some sort of printing mistake.

- 1 year, 7 months ago

×