MHB Counting problem involving numbered cards

[Milly]

How to solve ii (b) ? Thanks in advance.

 

[MarkFL]

Hello, Milly! :D

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[Milly]

I actually tried out by using 5P2 but it didn't work.

 

[soroban]

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