The probability that Alice and Bob form a match is [tex]^{24} C_{5}[/tex] * (([tex]^{24} C_{4}[/tex])*20*19) / [tex]^{24} C_{5}[/tex] * [tex]^{24} C_{5}[/tex].
To answer the question, we use the probability by its complement.
The complement of an event is the subset of outcomes in the sample space that are not in the event. A complement is itself an event.
In this case, probability space is ([tex]^{24} C_{5}[/tex])^2 where there is match for 4 or 5.
For number of ways for 5 adjectives match is ([tex]^{24} C_{5}[/tex]).
For number of ways for 4 adjectives match is ([tex]^{24} C_{4}[/tex])*20*19.
We first choose 4 adjectives which are match and then there are 20*19 ways for both of them to choose an adjective each from remaining 20 adjectives.
Then, the desired probability is:
[tex]^{24} C_{5}[/tex] * (([tex]^{24} C_{4}[/tex])*20*19) / [tex]^{24} C_{5}[/tex] * [tex]^{24} C_{5}[/tex]
Learn more about complement at: https://brainly.com/question/13723132
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