There is only 1 way to select the sequence 1,2,3 in that exact order. This is out of 720 different ways to select 3 cards at random where you don't put the card back and order matters. Where am I getting the 720? From this line of thinking:
Imagine we had 3 slots A, B, C. In slot A, we have 10 choices to pick from. After making a choice, we have 10-1 = 9 choices left. We can't put the card back. So we have 9 options for slot B. Then we have 8 for slot C. Multiply these values out and we get 10*9*8 = 720
At this point, we divide the values 1 over 720 to get the fraction 1/720
The probability as a fraction is 1/720 which converts to the decimal form 0.001389 which is approximate. This converts to 0.1389%; the chances of Annie picking the right sequence is very small.
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