Question

1. There are five wires which need to be attached to a circuit board. A robotic device will attach the wires. The wires can be attached in any order, and the production manager wishes to determine which order would be fastest for the robot to use. Use the multiplication rule of counting to determine the number of possible sequences of assembly that must be tested. (Hint: There are five choices for the first wire, four for the second wire, three for the third wire, etc. Enter an exact number.)

2. Compute P_5,2. (Enter an exact number.)

3. Compute C_7,2. (Enter an exact number.)

4. One professor grades homework by randomly choosing 5 out of 14 homework problems to grade.

(a) How many different groups of 5 problems can be chosen from the 14 problems? (Enter an exact number.)
groups

(b) Probability extension: Jerry did only 5 problems of one assignment. What is the probability that the problems he did comprised the group that was selected to be graded? (Enter a number. Round your answer to four decimal places.)

(c) Silvia did 7 problems. How many different groups of 5 did she complete? (Enter an exact number.)
groups

( d) What is the probability that one of the groups of 5 she completed comprised the group selected to be graded? (Enter a number. Round your answer to four decimal places.)

Answer 1