In how many ways may 5 same people line up if two of the people refuse to stand next to each other?
72
A multiple-choice test consists of 15 questions, each permitting a choice of 5 alternatives. In how many ways may a student fill in the answers if they answer each question?
515 = 30, 517, 578, 125
In how many ways can I create 2 letter words from the letters in the word DAVE? Any 2 letters form a 2 letter word.
16
A team of 8 basketball players needs to choose a captain and co-captain. How many ways are there to do this?
56
How many different committees of 5 people can be chosen from 10 people?
252
Among the seven nominees for two vacancies on the city council are three men and four women. In how many ways may these vacancies be filled with one of the men and one of the women?
12
5. Suppose a True-False test has 20 questions. a) In how many ways may a student mark the test, if each question is answered?
2^20=1048576
You will get a cell phone and you must decide on the right plan.There are 10 different phones, 6 different calling plans and 3 different texting plans, how many different plans could you pick from if you can choose 1phone, 1call, 1text plan
180
There are 110 people at a meeting. They each shake hands with everyone else. How many handshakes were there?
5995
The ski club with ten members is to choose three officers captain, co-captain & secretary, how many ways can those offices be filled?
720
Mr. Jones owns 4 pairs of pants, 7 shirts, and 3 sweaters. In how many ways may he choose 2 of the pairs of pants, 3 of the shirts, and 1 of the sweaters to pack for a trip?
630
How many permutations are there of the letters in the word “greet”?
60
In how many ways may can five persons line up to get on a bus?
120
You just bought 3 tickets to the Yankees and you have 5 friends you could invite. How many different combinations of friends could you choose to join you at the game?
10
Suppose you are asked to list, in order or preference, the three best movies you have seen this year. If you saw 10 movies during the year, in how many ways can the three best be chosen and ranked?
720
Selecting which seven players will be in the batting order on a 11 person team.
330
Suppose you find 7 articles related to the topic of your research paper. In how many ways can you choose 5 articles to read?
21
In how many ways may 8 people form a circle for a folk dance?
5040
How many unique 3 digit codes can be created from the 5 digits {1, 2, 3, 4, 5} if repeats are possible?
125
A group of 45 people are going to run a race. The top three runners earn gold, silver, and bronze medals.
85140
How many distinct permutations are there of the word “statistics”?
50, 400
The student body of 10 students wants to elect a president, vice president, secretary, and treasurer.
5040
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