-10- An instructor has 11 grade options for each student in a class of 16 studen

Question

-10- An instructor has 11 grade options for each student in a class of 16 students. His grade sheet lists the 16 names of his students. 10. a) In how many ways can the instructor fill in his grade sheet? b) How many if he gives 2 A+'s, 4 A's, 7 B's and 3 C's? The instructor decides to give prizes to three of his students -An apple, a textbook and an Iphone. How many ways can he do that? c) He is taking 6 students on a field trip, and is told to take an equal number of men and women on the trip. There are nine women in the class. How many total possible groups can be chosen for the field trip? d) (Turn over for last question!!!

Explanation / Answer

a) as each student has 11 choices of grade; number of ways =1116 =4.6*1016

b) number of ways =16!/(2!*4!*7!*3!) =14414400

c)

numebr of ways =N(select 3 student from 16 and then order them to get 3 different gifts) =16P3 =16!/(13)! =3360

d)

number of groups =N(3 male students from 7 male students and 3 female from 9 female)

=7P3 *9P3 =35*84 =2940

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