MHB Counting problem involving numbered cards

AI Thread Summary
The discussion focuses on solving a counting problem involving nine numbered cards, specifically how to determine the number of different three-digit numbers that can be formed between 200 and 300. The cards include duplicates, which complicates the counting process. Users are encouraged to share their attempted solutions to receive more targeted help. The simplest approach suggested is to list all possible combinations that meet the criteria. The final answer provided is that there are 22 different numbers that can be formed.
Milly
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How to solve ii (b) ? Thanks in advance.
 

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Hello, Milly! :D

I have given your thread a title that briefly describes the posted problem. A title like "Help :/" does not tell anyone viewing the thread listing anything about the nature of the question being asked, and it is assumed that help is being sought.

Can you post what you have tried so far, so that our helpers can see where you are stuck, or where you may be going wrong, and can offer better assistance?

Using good thread titles and showing effort are two of the things we ask from our users, as given in our http://mathhelpboards.com/rules/.
 
I actually tried out by using 5P2 but it didn't work.
 
Hello, Milly!

How to solve ii (b)?

7. Nine cards are numbered: 1, 2, 2, 3, 3, 4, 6, 6, 6.

(ii) Three of the nine cards are chosen and placed in a line,
. . .making a 3-digit number.

Find how many different numbers can be made in this way
(b) if the number is between 200 and 300.
The easiest solution is to simply list them.

. . \begin{array}{ccccc} 212 & 221 & 231 & 241 & 261 \\ 213 & 223 & 232 & 242 & 2 62 \\ 214 & 224 & 233 & 243 & 263 \\ 216 & 226 & 234 & 2 46 & 264 \\ && 236 && 266 \end{array}

Answer: 22
 
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