At a certain university, 7 students from the 10-student history department and 5 students from the 7-student English department will be selected to form a 12-student committee. At a neighboring university, 2 students from a 10-person math department and 3 students from a 7-student science department will be selected to form a 5-student focus group. What is the ratio of the number of ways in which the 12-student committee can be formed to the number of ways in which the 5-student focus group can be formed? Options
A) 25/16	B) 8/5	C) 12/5	D) 16/5	E) 144/25
Number of ways of selecting a 12 member student committee = 10C7 * 7C5   Number of ways of selecting a focus group of 5 students = 10C2 * 7C3   Ratio of 12 member student committee to 5 member focus group = 10C7∗7C5/10C2∗7C3= 8585   Answer: 8/5
<result>B</result>
At a certain university, 7 students from the 10-student history department and 5 students from the 7-student English department will be selected to form a 12-student committee. At a neighboring university, 2 students from a 10-person math department and 3 students from a 7-student science department will be selected to form a 5-student focus group. What is the ratio of the number of ways in which the 12-student committee can be formed to the number of ways in which the 5-student focus group can be formed?