In the permutation group S2021, a product of all transpositions (where each transposition occurs exactly once) is always an even permutation.

P29.10 Determine the number of permutations of size 3 that can be made from the set {1, 2, 3, 4, 5, 6}. Write down all of the permutations.

Many states have a lottery game, usually called Pick-4, in which you pick a four-digit number such as 7359. During the lottery drawing, there are four bins, each containing balls numbered 0 throug 9. One ball is drawn from each bin to form the four gigit winning number. There are many variations of this game. The primary variation allows you to win if the four digits in your numuber are selected in any order as long as they are the same four digits as obtained by the lottery agency. For example, if you pick four digits makng the number 1265, then you will win if 1265, 2615, 5216, 6521, and so forth, are drawn, The variations of lottery game depend on how many unique digits are in your umber. Consider the following four different versions of this game. Find the proability: 4) One digit appears three times

There are eight 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 eight choices for the first wire, seven for the second wire, six for the third wire, etc.)