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100
A lock has 30 numbers. How many different combinations for the lock are there if it uses 3 numbers and the numbers can be repeated?
30*30*30 = 27, 000
100
How many permutations are there of the letters in the word "great"?
5! = 120
100
How many ways can six different books be arranged on a shelf if one of the books is an encyclopedia and it must last?
5! = 120
100
How many different ways can a five-question true-false test be answered?
2*2*2*2*2 = 32
100
The menu for a banquet has a choice of two types of salad, five main courses, and three desserts. How many ways can a salad, main course, and dessert be selected to form a meal?
2*5*3 = 30
200
How many permutations are there of the letters in the word "greet"?
5!/2! = 60
200
Consider making a four-digit I.D. number using the digits 2, 4, 7, and 0. How many can be formed if repetition is allowed, but 0 is not used first?
3*4*4*4 = 192
200
How many ways can 1st, 2nd, and 3rd place be picked from 5 people in a hot dog eating contest?
5*4*3 = 60
200
Your summer reading list has 30 books to choose from. You must choose 4 of those books to read and write a book report on. How many different sets of 4 books could you read?
30 C 4 = 27,405
200
In how many ways can ten people wait in line to enter Target for Black Friday sales at 5 in the morning?
10! = 3, 628, 800
300
Try-outs for this season's American Idol competition have already been held. During try-outs, all potential idols start out by approaching an intern as a group of 4 and singing 10 to 20 seconds of a song. If 5000 people show up to audition in the twin cities, how many combinations of 4 would be possible for the interns to hear?
5000 C 4
300
How many different arrangements of the word "popcorn" can be made if the first and last letter must stay the same?
5!/2! = 60
300
An art collector, who owns 10 original paintings, is preparing a will. In how many ways may the collector leave these paintings to three heirs?
10 P 3 = 720
300
How many ways can five letters be chosen from the English alphabet?
26 C 5 =65,780
300
There are five finalists in the American Ice Skating competition that are trying to make it onto the United States olympic team. The top two skaters will make the team. How many pairings of skaters could the U.S. send to the olympics?
5 C 2
400
Assume that 26 books, consisting of 8 identical mathematics texts, 6 identical computer science texts, 9 identical physics books, and 3 identical chemistry texts are to be placed on a shelf. How many distinct ways can they be placed on the shelf?
26! / (8!*6!*9!*3!) = 6.38 X 10^12
400
The 7 book Harry Potter series is very popular in the local elementary school library. The books are kept on a shelf and very frequently are put back in a random order. What is the probability that the books happen to be in the correct order?
1/7! = 1/5040
400
How many ways can a committee of 4 men and 5 women be selected from a group of 10 men and 20 women?
10C4 * 20C5 = 3,255,840
400
A carton contains 12 eggs, 2 of which are cracked. If we randomly select 5 of the eggs for hard boiling, how many combinations of all good eggs can be selected?
10C5 = 252
400
How many ways can 12 colored cages be arranged around a ferris wheel if 4 cages are green, 4 cages are blue, and 4 cages are red?
12!/ (4!4!4!) = 34,650
500
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?
4C2 * 7C3 *3C1 = 6*35*3 = 630
500
In California's Super Lotto Plus lottery game, winning the jackpot requires that you select the correct five numbers between 1 and 47 inclusive and, in a separate drawing, you must also select the correct single number between 1 and 27 inclusive. Find the probability of winning the jackpot.
1/(47C5 * 27) = 1/41,416,353
500
A carton contains 12 eggs, 2 of which are cracked. If we randomly select 5 of the eggs for hard boiling, what is the probability that all of the cracked eggs are selected?
1/(2C2 *10C3) = 1/120
500
Among the seven nominees for three 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 two of the women?
3*4P2 = 36
500
Consider having a ferris wheel with 12 DIFFERENT colored cages. How many ways can the cages be arranged on the ferris wheel if two of the cages must be next to eachother?
22*10! = 79,833,600
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