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## What is Permutation ?

Permutation is the act of arranging the members of a set into a sequence or order, or, if the set is already ordered, rearranging (reordering) its elements—a process called permuting.

## Try the problem from AMC 10B – 2020 – Problem 5

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.)

A) 210 B) 420 C) 630 D) 840 E) 1050

Source
Competency
Difficulty
Suggested Book

American Mathematics Competition 10 (AMC 10B), 2020, Problem Number – 5

Permutation

5 out of 10

Mathematical Circle

## Use some hints

First hint

If you really need a hint you can go through the concept of probability at first : In its simplest form, probability can be expressed mathematically as: the number of occurrences of a targeted event divided by the number of occurrences plus the number of failures of occurrences (this adds up to the total of possible outcomes):

$p(a) = \frac {p(a)} { [P(a) + p(b)] }$

Second Hint

Let’s try to find how many possibilities there would be if they were all distinguishable, then divide out the ones we over counted . 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 for green tiles.

Final Step

I am sure that you are almost there for the final calculation but let me help those who are still not there

$\frac {7!}{6 \cdot 2} = 420$ .

So the correct answer is B) 420