# Research in school

For particular research in high school, four pupils are to be selected from a class with 30 pupils. Calculate the number of all possible results of the select and further calculate the number of all possible results, if it depends on the order in which the students come to the interview.

Correct result:

n1 =  27405
n2 =  657720

#### Solution:

$C_{{ 4}}(30)=\dbinom{ 30}{ 4}=\dfrac{ 30! }{ 4!(30-4)!}=\dfrac{ 30 \cdot 29 \cdot 28 \cdot 27 } { 4 \cdot 3 \cdot 2 \cdot 1 }=27405 \ \\ \ \\ n_{1}={ { 30 } \choose 4 }=27405$
$n_{2}=30 \cdot \ 29 \cdot \ 28 \cdot \ 27=657720$

We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!

Tips to related online calculators
Would you like to compute count of combinations?

## Next similar math problems:

• Tournament
Six teams entered the basketball tournament. How many matches will be played if each team has to play one match with each other?
• Three reds
What is the probability that when choosing 3 carats from seven carats, all 3 reds will be red?
How many ways can we thread 4 red, 5 blue, and 6 yellow beads onto a thread?
• Raffle
There are 200 draws in the raffle, but only 20 of them win. What is the probability of at least 4 winnings for a group of people who have bought 5 tickets together?
• Sum or product
What is the probability that two dice fall will have the sum 7 or product 12?
• Cards
From a set of 32 cards we randomly pull out three cards. What is the probability that it will be seven king and ace?
• Families 2
There are 729 families having 6 children each. The probability of a girl is 1/3 and the probability of a boy is 2/3. Find the the number of families having 2 girls and 4 boys.
• Two groups
The group of 10 girls should be divided into two groups with at least 4 girls in each group. How many ways can this be done?
• Three workplaces
How many ways can we divide nine workers into three workplaces if they need four workers in the first workplace, 3 in the second workplace and 2 in the third?
• Boys and girls
There are eight boys and nine girls in the class. There were six children on the trip from this class. What is the probability that left a) only boys b) just two boys
• Word MATEMATIKA
How many words can be created from the word MATEMATIKA by changing the order of the letters, regardless of whether or not the words are meaningful?
• Boys and girls
There are 11 boys and 18 girls in the classroom. Three pupils will answer. What is the probability that two boys will be among them?
• STRESSED word
Each letter in STRESSED is printed on identical cards, one letter per card and assembled in random order. Calculate the probability that the cards spell DESSERTS when assembled.