The policy committee at the state university has 6 members, LaToyna, Ming, Jose,

Question

The policy committee at the state university has 6 members, LaToyna, Ming, Jose, John, Prof. Rise, and Dr. hernandez. A subcommittee of two members must be formed to investigate the visitation policy in the dormitories. List all possible simple random samples of size 2.

A. LaToyna and Ming, Jose and John, Prof. Rise and Dr. Hernandez

B. LaToyna and Ming, LaToyna and Jose, LaToyna and John, LaToyna and Prof. Rise, LaToyna and Dr. Hernandez, Ming and Jose, Ming and John, Ming and Prof. Rise, Ming and Dr. hernandez, Jose and John, Jose and Dr. Hernandez, John and Prof. rise, John and Dr. Hernandez, Prof rise and Dr Hernandez

C. LaToyna and Ming, Ming and Jose, Jose and John, John and Prof. Rise, Prof. Rise and Dr. Hernandez

D. Latoyna and Ming, Latoyna and Jose, Latoyna and John, Latoyna and Prof. Rise, Latoyna and Dr. Hernandez

Explanation / Answer

AS GIVEN WE HAVE TOTAL 6 AND WE NEED TO FORM GROUP OF SIZE 2

THE TOTAL WAYS IN THIS CAN BE DONE = 6C2 = 6!/(2!*4!) = 15 WAYS

TO AS PER THE GIVEN NAMES THE TOTAL COMBINATIONS ARE = LaToyna and Ming, LaToyna and Jose, LaToyna and John, LaToyna and Prof. Rise, LaToyna and Dr. Hernandez, Ming and Jose, Ming and John, Ming and Prof. Rise, Ming and Dr. hernandez, Jose and John, Jose and Dr. Hernandez, John and Prof. rise, John and Dr. Hernandez, Prof rise and Dr Hernandez

HENCE OPTION B IS CORRECT

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