How many ways can a $3$-person subcommittee be selected from a committee of $7$ people? How many ways can a president, vice-president, and secretary be chosen from a committee of $7$ people?

The sample space for tossing 3 coins consists of how many outcomes?

a. 2

c. 6

b. 4

d. 8

From a standard 52 -card deck, find how many 5 -card hands are possible that have: 3 hearts and 2 clubs.

An ordinary deck of playing cards has 52 cards. There are four suits-spades, hearts, diamonds, and clubs-with 13 cards in each suit. Spades and clubs are black; hearts and diamonds are red. If one of these cards is selected at random, what is the probability that it is a. a spade? b. red? c. not a club?

In a horse race, how many different finishes among the first 3 places are possible if 10 horses are running? (Exclude ties.)

How many ways can a president, vice president, treasurer, and secretary be picked from 15 students?

On an English test, Tito must write an essay for three of the five questions in Part 1 and four of the six questions in Part 2 in any order. How many different combinations of questions can be answer?

A small combination lock has $3$ wheels, each labeled with the $10$ digits from $0$ to $9$. If an opening combination is a particular sequence of $3$ digits with no repeats, what is the probability of a person guessing the right combination?

How many ways are there to select a subcommittee of 5 members from among a committee of 12?

A 4-person grievance committee is selected out of 2 departments A and B, with 15 and 20 people, respectively. In how many ways can the following committees be selected? (A) 3 from A and 1 from B (B) 2 from A and 2 from B (C) All from A (D) 4 people regardless of department (E) At least 3 from department A.

A survey of 800 small businesses indicates that 250 own a video conferencing system, 420 own projection equipment, and 180 own a video conferencing system and projection equipment. (A) How many businesses in the survey own either a video conferencing system or projection equipment? (B) How many own neither a video conferencing system nor projection equipment? (C) How many own projection equipment and do not own a video conferencing system?

How many ways can a president vice-president and secretary be chosen from a club with $10$ members?

A small combination lock has 3 wheels, each labeled with the 10 digits from 0 to 9. How many 3-digit combinations are possible if no digit is repeated? If digits can be repeated? If successive digits must be different?

In SuperLotto Plus, a California state lottery game, you select five distinct numbers from $1$ to $47$, and one MEGA number from $1$ to $27$, hoping that your selection will match a random list selected by lottery officials. (a) How many different sets of six numbers can you select? (b) Paul Burke always includes his age and his wife's age as two of the first five numbers in his SuperLotto Plus selections. How many ways can he complete his list of six numbers?