1. There are 4 routes from A to B, 8 routes from B to C, and 12 routes from C to D. How many routes are there from A to D if we must pass B and C?

2.The gate code to a gated community consists of the # key, followed by 4 letters chosen from the English alphabet, followed by 7 digits. What is the total number of possible gate codes?

3.Professor Hermann gives his class 12 potential test questions, he will then put 5 of the 12 questions on the real test. In how many ways can Professor Hermann make up the test?

4.Ms. Goodman has 19 students in her first-grade class. In how many ways can 4 students be picked to help Ms. Goodman tidy up the classroom after school?

5.A coin is flipped 9 times and the sequence of heads and tails recorded. In how many ways can a sequence consist of exactly 3 heads and the rest tails?

6.A tablet, a yo-yo, and a box of chocolates will be given to 3 randomly picked people out of 31 who attend a pyramid scheme indoctrination session. In how many ways can the 3 people be picked?

7. 41 Ponzi schemers are on the government's hit-list. In how many ways can the government name 3 of them as the number one, number two, and number three most evil Ponzi schemer?

8. 19 math teachers attend a presentation on Group Study Skills. During the presentation the presenter divides all the attendees into 4 groups for group discussion. The first group consists of 3 people, the second group 4, the third group 5, and the fourth group the remaining people. In how many ways can the groups be formed?

9. 16 blue and 17 green raffle tickets are in a box. A sample of 7 tickets are drawn. In how many ways can the sample consist of 4 blue and 3 green tickets?

10. 7 members from the math department, 7 members from the biology department, 7 members from the English department, 7 members from the history department, and 7 members from the physics department have declared themselves candidates for three vacant faculty senate seats. If the three seats must be filled by three members from three different departments, in how many ways can the vacant seats be filled?

11.Use the Gauss-Jordan method to solve the system. Write down all steps. You will need to upload your work in the last question of this test in order to be graded.

\fxty=18 16 (3,15) VS-x+10 14 O 120 12 12 - X 10 (0,10) 6 -4 2 (0,0) 0 2 4 6 8 10 12 14 16 18