# Difference between revisions of "2020 AMC 10B Problems/Problem 5"

## Problem

How many distinguishable arrangements are there of 1 brown tile, 1 purple tile, 2 green tiles, and 3 yellow tiles in a row from left to right? (Tiles of the same color are indistinguishable.) $\textbf{(A)}\ 210 \qquad\textbf{(B)}\ 420 \qquad\textbf{(C)}\ 630 \qquad\textbf{(D)}\ 840 \qquad\textbf{(E)}\ 1050$

## Solution

Let's first find how many possibilities there would be if they were all distinguishable, then divide out the ones we overcounted.

There are $7!$ ways to order $7$ objects. However, since there's $3!=6$ ways to switch the yellow tiles around without changing anything (since they're indistinguishable) and $2!=2$ ways to order the green tiles, we have to divide out these possibilities. $\frac{7!}{6\cdot2}=\boxed{\textbf{(B) }420}$ ~quacker88

## Solution 2 (2 second solve)

Assume that MAA is an immature bunch and guess $\boxed{\textbf{(B) }420}$, which happens to be the correct answer. -fidgetboss_4000

## Video Solution

~IceMatrix

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 