Factorial - practice problems
The factorial of the number n is the product of the first n natural numbers. For example 6! (we read 6 factorial) is 1*2*3*4*5*6 = 720.
Directions: Solve each problem carefully. Show all your work.
Number of problems found: 140
- Factorial divisible by 75
Find the least positive integer n such that n! is divisible by 75. - Five couples
In how many ways can 5 couples arrange themselves in a row if they stay together? - Student examination
How many ways can a teacher select a group of 6 students to sit in the front row if the class has 13 students? - On the windowsill
On the windowsill, 6 different flowers in flower pots are to be arranged next to each other. Four are flowering (one of them is a primrose), the rest are decorative with leaves (one of them is a fern). Determine: a) how many different arrangements can be - Footballers 2
Footballers have jerseys numbered 7, 8, 9, 10, and 11. The coach wants to send them to attack: a) so that no two even-numbered jerseys are adjacent, b) so that no two odd-numbered jerseys are adjacent. How many options does he have in each case? - In the library
We have 8 different books in a library. In how many ways can they be arranged? In how many ways can they be arranged if 3 specific volumes must appear in a fixed given order? In how many ways can they be arranged if three specific volumes must appear cons - Birthday boy 2
In how many ways can seven people be seated around a table if the birthday boy must sit at the head? - HAMMER 3
Determine in how many ways the letters of the word HAMMER can be rearranged so that some group of consecutive letters in the rearrangement forms the word WATER. - Relay
A relay race will be run by the class team of Kate, Alice, Michaela, and Erica. Determine how many different running orders are possible, given that each of them can run in any position. - Grouping - combinatorics
In how many different ways can 24 people be divided into: a) 6 groups of the same size. b) Groups of 5, 6, 7, and 6 people. c) Groups of 4, 5, 7, and 8 people. - Refrigerator, lemonades
How many possible ways can we store three lemonades, four mineral waters, and two juices in the refrigerator next to each other? - Married pairs
In how many ways can we seat five guests at a table, two of whom are married and want to sit next to each other? - Cancel variations
Evaluate the following expression with factorials: (45!-44!)/(44!) - Probability - shelf
Ten books are placed randomly on one shelf. Find the probability that certain three books are placed next to each other. - Permutation element count
From how many elements can we make 5040 permutations without repetition? - Flag color combinations
How many 4 colored flags can be made from 5 colors so that each flag consists of three different colors? - Aquaristics
We consider 'words' (i.e., arbitrary strings of letters) obtained by rearranging the letters of the word 'AQUARISTICS'. All letters are treated as distinguishable from each other. The number of such words that also contain the string 'CAVA' (as consecutiv - SKMO Patricia had written natural numbers from 1 to 9. She added two of these numbers, deleted them, and wrote the resulting sum instead of the summaries. She thus had eight numbers written down, which she managed to divide into two groups with the same produc
- Natural numbers
Find the number of all natural numbers greater than 200 in which the digits 1, 2, 4, 6, 8 occur at most once and not contains any other digits. - Compartment ball options
We have eight compartments where we put three indistinguishable balls and two distinguishable ones. How many options do we have?
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