# 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?

Result

n =  462

#### Solution:

$C_{{ 4}}(10)=\dbinom{ 10}{ 4}=\dfrac{ 10! }{ 4!(10-4)!}=\dfrac{ 10 \cdot 9 \cdot 8 \cdot 7 } { 4 \cdot 3 \cdot 2 \cdot 1 }=210 \ \\ \ \\ C_{{ 5}}(10)=\dbinom{ 10}{ 5}=\dfrac{ 10! }{ 5!(10-5)!}=\dfrac{ 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 } { 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 }=252 \ \\ \ \\ n={ { 10 } \choose 4 } + { { 10 } \choose 5 }=462$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
Be the first to comment!

Tips to related online calculators
See also our combinations with repetition calculator.
Would you like to compute count of combinations?
See also our variations calculator.

## Next similar math problems:

1. Birthday paradox
How large must the group of people be so that the probability that two people have a birthday on the same day of the year is greater than 90%?
2. Boys and girls
There are 20 boys and 10 girls in the class. How many different dance pairs can we make of them?
3. Graduation party
There are 15 boys and 12 girls at the graduation party. Determine how many four couples can be selected.
4. Divide
How many different ways can three people divide 7 pears and 5 apples?
5. Birth
Let's assume that the probability of the birth of a boy and a girl in the family is the same. What is the probability that in a family with five children, the youngest and oldest child is a boy?
6. Beads
How many ways can we thread 4 red, 5 blue, and 6 yellow beads onto a thread?
7. Gold, silver, bronze
How many ways can we divide gold, silver, bronze medails if there are 6 people competing?
8. Twenty-five
How many three-digit natural numbers are divisible by 25?
9. The test
The test contains four questions, and there are five different answers to each of them, of which only one is correct, the others are incorrect. What is the probability that a student who does not know the answer to any question will guess the right answer
10. Recruitment
11. Five letters
How many ways can five letters be arranged?
12. Fall sum or same
Find the probability that if you roll two dice, it will fall the sum of 10, or the same number will fall on both dice.
13. The university
At a certain university, 25% of students are in the business faculty. Of the students in the business faculty, 66% are males. However, only 52% of all students at the university are male. a. What is the probability that a student selected at random in t
14. Possible combinations - word
How many ways can the letters F, A, I, R be arranged?
15. Cube construction
A 2×2×2 cube is to be constructed using 4 white and 4 black unit cube. How many different cubes can be constructed in this way? ( Two cubes are not different if one can be obtained by rotating the other. )
16. Dice and coin
A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the probability that the number rolled is greater than 2 and the coin toss is head?
17. One three
We throw two dice. What is the probability that max one three falls?