Question 854713
7 slips of paper, each slip references one day of the week.
the weekend therefore is contained in two of these slips.


the probability that you will get 0 classes on the weekend is 5/7 * 4/6 = 20/42 = 10/21.


this is because 5 out of the 7 days are not on the weekend.


the number of ways you can get 2 slips of paper out of 7 is equal to 7C2 which is equal to (7*6) / 2 which is equal to 21.


the number of ways you can get 2 out of 5 days that are not weekends is 5C2 which is equal to 5*4 / 2 which is equal to 20 / 2 which is equal to 10.


the probability is therefore equal to 5C2 / 7C2 which is equal to 10/21 that you will not get a weekend day.


this is small enough that i can show you all the different arrangement.


let the letters a and b represent the weekend days.


let the number 1,2,3,4,5 represent the weekday days.


the pot contains a,b,1,2,3,4,5


you draw 2 slips of paper at a time.


the possible combinations are:


ab ***** 
a1 *****
a2 *****
a3 ***** 
a4 ***** 
a5 ***** 


b1 *****
b2 *****
b3 *****
b4 *****
b5 *****


12
13
14
15


23
24
25


34
35


45


out of the 21 possible pairs, 11 of them contain a weekend day.
this means there are 10 pairs that do not contain a weekend day.


the probability that you will not have a class on the weekend is 10/21.