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:

C4(10)=(104)=10!4!(104)!=109874321=210  C5(10)=(105)=10!5!(105)!=10987654321=252  n=(104)+(105)=462C_{{ 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:
1st comment
Be the first to comment!
avatar




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
    holland 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
    dancers There are 20 boys and 10 girls in the class. How many different dance pairs can we make of them?
  3. Graduation party
    dancers There are 15 boys and 12 girls at the graduation party. Determine how many four couples can be selected.
  4. Divide
    hrusky How many different ways can three people divide 7 pears and 5 apples?
  5. Birth
    probability 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
    koralky2 How many ways can we thread 4 red, 5 blue, and 6 yellow beads onto a thread?
  7. Gold, silver, bronze
    olympics How many ways can we divide gold, silver, bronze medails if there are 6 people competing?
  8. Twenty-five
    prime How many three-digit natural numbers are divisible by 25?
  9. The test
    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
    numbers_1
  11. Five letters
    charH How many ways can five letters be arranged?
  12. Fall sum or same
    dices2 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
    family_1 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
    dices2 How many ways can the letters F, A, I, R be arranged?
  15. Cube construction
    222cube 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
    dice 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
    dice We throw two dice. What is the probability that max one three falls?