Hi,

7 slips, 2 chosen w/o replacement, 5 weekdays

P(no classes is scheduled at the weekend) = P(scheduled on weekday) =  

Note: 

Ex.  5C2 = 

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
 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.





 

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