How many 3-digit passcodes are possible if digits, chosen from the set 0, 1, 2, 3, 4, 5, 6cannot be repeated, and the first digit must be an odd number?

A software development group uses randomly generated computer file names for security. If each name must be created by selecting two letters, with repeats allowed, from the set a, b, c, d followed by three digits, repeats not allowed, from the set of numbers1, 2, 3, 4, 5, 6, 7, how many filenames can be created?

At a local ice cream shop, customers can choose from 19 flavors of ice cream. A customer wants to purchase a 3- scoop ice cream cone. How many ways can the customer select the flavors if no flavor may be repeated, but the order of the flavors on the cone is important?

How many ways can 3 different contracts be distributed among 8 different companies if a company can be awarded more than one contract?

In the card game Crazy Eights, players are dealt 8 cards from a standard deck of 52. How many different ways can a player be dealt seven cards?

A 6-member coed volleyball team is chosen from a group of 9 men and 7 women. If there must be at least one member of each gender on the team, how many different ways can the team members be chosen?

Suppose each person in a class of 47 students shakes hands with everyone else. How many handshakes will be made?

Suppose set S has a cardinal number of 9

a. How many subsets can be formed from the set?

b. How many subsets containing 5 elements can be formed from the set?

How many different words can be formed using all of the letters in STATISTICS?