This is a great question!
To determine the probability with which two sweets are not the same, you would have to subtract the probability with which two sweets are the same from 1. That would only be possible if she chose 2 liquorice sweets, 5 mint sweets and 3 humburgs -
As you can see, the first time you were to choose a Liquorice, there would be 12 out of the 20 sweets present. After taking that out however, there would be respectively 11 Liquorice out of 19 remaining. Apply the same concept to each of the other sweets -
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Calculate the probability of drawing 2 of each, add them together and subtract from one to determine the probability that two sweets will not be the same type of sweet!
<u><em>Thus, the probability should be 111 / 190</em></u>