. ( 3 ) A group of 20 students under review for the dean \'s list . The dean \'s

Question

. ( 3 ) A group of 20 students under review for the dean 's list . The dean 's list consists of 10 students . a . How many different dean 's lists are there ? b . Among these 10 , 3 will be chosen for the provost 's list and one of these 3 will receive the president 's award . How many different winning combinations are there ? C. Suppose the 20 students are made up of 12 freshmen and 8 sophomore , and this year it is the freshmen 's turn to receive the president 's award , how many different winning combinations are there ? . ( 3 ) A group of 20 students under review for the dean 's list . The dean 's list consists of 10 students . a . How many different dean 's lists are there ? b . Among these 10 , 3 will be chosen for the provost 's list and one of these 3 will receive the president 's award . How many different winning combinations are there ? C. Suppose the 20 students are made up of 12 freshmen and 8 sophomore , and this year it is the freshmen 's turn to receive the president 's award , how many different winning combinations are there ?

Explanation / Answer

Here' how to answer the question:

a. There can be 20 choose 10 or 20C10 = 184756 differnt dean' list

b. Ways this can be done: Out of 20 choose 10 for dean' list * From dean' list pull 3 for provost' * Out of the 3 pull 1 for president' = 20C10 *10C3*3C1 = 66512160 ways this can be done

c. We will choose 1 freshman out of the 12 for president' award. So, 12C1 ways.

And the rest 19 will be used to select 9 other dean' list winners.

So, 12C1 * 19C9 = 1108536 ways

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