Here the sampling is without replacement, and we can take it to be either ordered or unordered; the answers will be the same. For ordered samples, the size of the= 7·6·5 = 210. If A is the event ‘no lectures at weekends’, then A occurspreciselywhenallthreedaysdrawnareweekdays;so|A|=5P =5·4·3=60.
Thus, P(A) = 60/210 = 2/7.
If we decided to use unordered samples instead, the answer would be 5C3/7C3,
with replacement
without replacement
ordered sample
Nn
NPn
unordered sample
NCn
sample space is 7P3
which is once again 2/7.