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MATH / How many distinguishable ways are there to write 9 as the sum of 1's, 2's, and 4's, where the order of the addends matters? For example, 4+4+1 and 1+4+4 are two different ways.

Problem

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problem

How many distinguishable ways are there to write 99 as the sum of 1's,1\text{'s}, 2's,2\text{'s}, and 4's,4\text{'s}, where the order of the addends matters? For example, 4+4+14 + 4 + 1 and 1+4+41 + 4 + 4 are two different ways.
Plain-text mathematical notation (without MathML)
How many distinguishable ways are there to write 9 as the sum of 1's, 2's, and 4's, where the order of the addends matters? For example, 4+4+1 and 1+4+4 are two different ways.
Original LaTeX notation
How many distinguishable ways are there to write $9$ as the sum of $1\text{'s},$ $2\text{'s},$ and $4\text{'s},$ where the order of the addends matters? For example, $4 + 4 + 1$ and $1 + 4 + 4$ are two different ways.

level

Level 5

type

Counting & Probability

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Source and history

task_id
1a50a8a6-47c4-5765-945c-1898eb864da0
task_key
counting~5fand~5fprobability--test--1a50a8a6-47c4-5765-945c-1898eb864da0
task_revision_id
1
config / split
counting_and_probability / test

Official source

initial import