Question

Compute C_10,2.

Barbara is a research biologist for Green Carpet Lawns. She is studying the effects of fertilizer type, temperature at time of application, and water treatment after application. She has twofertilizer types, four temperature zones, and four water treatments to test. Determine the number of different lawn plots she needs in order to test each fertilizer type, temperature range, and water treatment configuration.

The University of Montana ski team has seven entrants in a men's downhill ski event. The coach would like the first, second, and third places to go to the team members. In how many ways can the seven team entrants achieve first, second, and third places?

There are four 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 four choices for the first wire, three for the second wire,  two for the third wire, etc.)

Answer 1

Result:

Compute C_10,2.

10C2=45

Barbara is a research biologist for Green Carpet Lawns. She is studying the effects of fertilizer type, temperature at time of application, and water treatment after application. She has two fertilizer types, four temperature zones, and four water treatments to test. Determine the number of different lawn plots she needs in order to test each fertilizer type, temperature range, and water treatment configuration.

number of different lawn plots =2*4*4 =32

The University of Montana ski team has seven entrants in a men's downhill ski event. The coach would like the first, second, and third places to go to the team members. In how many ways can the seven team entrants achieve first, second, and third places?

This is problem of permutation.

7P3=210

There are four 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 four choices for the first wire, three for the second wire,  two for the third wire, etc.)

The number of possible sequences = 4P4 = 24 ways.