Homework Sourse3 A group of 20 students under review for the dean s list
. ( 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 ?
Solution
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
