A search engine randomly orders the top ten results of a search and displays thr

Question

A search engine randomly orders the top ten results of a search and displays three of these as “prime searches” ordered as first, second, and third recommendations. part a. How many possible ways might the “prime searches” be displayed? part b. If Holly’s Hardware is in the top ten results, how many “prime searches” lists include Holly’s Hardware as one of the three recommendations? parts c and d. What is the probability that Holly’s Hardware is in the “prime searches”? (Answer as a fraction in lowest terms.) /

Explanation / Answer

(a) (10C3)*(3!) = ( (10!) / (3! * 7!) ) * (3!) = 720

(b) (9C2)*(3!) = ( (9!) / (2! * 7!) ) * (3!) = 216

(c-d) probabilty= 216/720 = 14/45

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