1- Winning the jackpot in a particular lottery requires that you select the correct five numbers between 1 and 28 and, in a separatedrawing, you must also select the correct single number between 1 and 35. Find the probability of winning the jackpot.

The probability of winning the jackpot is ____

2- A corporation must appoint apresident, chief executive officer(CEO), chief operating officer(COO), and chief financial officer(CFO). It must also appoint a planning committee with four different members. There are 12 qualifiedcandidates, and officers can also serve on the committee. Complete parts(a) through(c) below.

a. How many different ways can the officers beappointed?

a. How many different ways can the officers beappointed?

There are __________ different ways to appoint the officers.

b. How many different ways can the committee beappointed?

There are _________different ways to appoint the committee.

c. What is the probability of randomly selecting the committee members and getting the three youngest of the qualifiedcandidates?

P(getting the three youngest of the qualified candidates)=

(Type an integer or a simplifiedfraction.)

3- With a short time remaining in theday, a delivery driver has time to make deliveries at 3 locations among the 8 locations remaining. How many different routes arepossible?

There are ___________ possible different routes.

4- Use the following results from a test for marijuanause, which is provided by a certain drug testing company. Among 142 subjects with positive testresults, there are 24 false positiveresults; among 154 negativeresults, there are 4 false negative results. If one of the test subjects is randomlyselected, find the probability that the subject tested negative or did not use marijuana.(Hint: Construct atable.)