In this task, you need to provide the correct option for a given problem from the provided options.
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Question: Problem: there are 12 slate rocks , 16 pumice rocks , and 8 granite rocks randomly distributed in a certain field . if 2 rocks are chosen at random and without replacement , what is the probability that both rocks will be slate rocks ?
Options: a ) 3 / 32 , b ) 7 / 64 , c ) 11 / 105 , d ) 15 / 127 , e ) 19 / 134

Answer: c

Question: Problem: a certain university will select 1 of 6 candidates eligible to fill a position in the mathematics department and 2 of 9 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 216 , b ) 212 , c ) 214 , d ) 210 , e ) 120

Answer: a

Question: Problem: the sum of the numbers is 177 . if the ratio between the first and the second be 5 : 3 and that between the second and third be 4 : 9 , then find the second number ?
Options: a ) 12 , b ) 20 , c ) 45 , d ) 60 , e ) 52

Answer:
c