Consider 6 classes, each consisting of 50 students. From this group of 300 stude

Question

Consider 6 classes, each consisting of 50 students. From this group of 300 students, a group of 6 students is to be chosen. (You can leave your answer in the format of n x without calculating numerical values)

(a) (6 points) How many choices are possible?

(b) (6 points) How many choices are there in which all 6 students are in the same class?

(c) (8 points) How many choices are there in which 5 of the 6 students are in the same class and the other student is in a different class?

Please include detail solutions! Thanks!!!

Explanation / Answer

6 DIFFERENT CLASS AND 50 EACH STUDENT IN EACH CLASS

TOTAL 300 STUDENTS

GROUP OF 6 TO BE PICKED

A) 6 TO BE PICKED AMONG 300 = 300C6 = 300!/(294!*6!) = 962822846700

B) IF ALL 6 ARE TO BE FROM SAME CLASS = 50C6 = (50!)/(44!*6!) = 15890700 THIS NUMBER IS FROM THE SAME CLASS

AS WE HAVE 6 DIFFERENT CLASSES THEREFORE THE ACTUAL NUMBER WILL BE 6*15890700 = 95344200

C)5 STUDENT FROM SAME CLASS = 50C5 = 2118760

BUT WE HAVE 6 DIFFERENT CLASS = 6*2118760 = 12712560

ALSO WE CAN CHOSE THE LAST ONE FROM 5 DIFFERENT CLASS

SO THE ACTUAL ANSWER WILL BE =12712560+5 = 12712565

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