The names of the seven days of the week are placed in a hat. Three names are drawn out; these will be the days of the Probability I lectures. What is the probability that no lecture is scheduled at th

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.