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!(10−4)!=10⋅9⋅8⋅74⋅3⋅2⋅1=210  C5(10)=(105)=10!5!(10−5)!=10⋅9⋅8⋅7⋅65⋅4⋅3⋅2⋅1=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

Try another example






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




Following knowledge from mathematics are needed to solve this word math problem:

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. Trinity
    trojka How many different triads can be selected from the group 43 students?
  2. Division
    skauti_3 Division has 18 members: 10 girls and 6 boys, 2 leaders. How many different patrols can be created, if one patrol is 2 boys, 3 girls and 1 leader?
  3. Disco
    vencek On the disco goes 12 boys and 15 girls. In how many ways can we select four dancing couples?
  4. Competition
    sutaz 15 boys and 10 girls are in the class. On school competition of them is selected 6-member team composed of 4 boys and 2 girls. How many ways can we select students?
  5. Cinema
    stale_kvoka How many ways can be divided 11 free tickets to the premiere of "Jáchyme throw it in the machine" between 6 pensioners?
  6. Menu
    jedalnicek On the menu are 12 kinds of meal. How many ways can we choose four different meals into the daily menu?
  7. Salami
    salama How many ways can we choose 5 pcs of salami if we have 6 types of salami for 10 pieces and one type for 4 pieces?
  8. Word MATEMATIKA
    math_1 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?
  9. Hockey game
    Hockey In the hockey game was made 6 goals. Czech played against Finland. Czechs won 4:2. In what order to fall goals? How many game sequence was possible during the game?
  10. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  11. A student
    test_14 A student is to answer 8 out of 10 questions on the exam. a) find the number n of ways the student can choose 8 out of 10 questions b) find n if the student must answer the first three questions c) How many if he must answer at least 4 of the first 5 que
  12. Mumbai
    Mumbai A job placement agency in Mumbai had to send ten students to five companies two to each. Two of the companies are in Mumbai and others are outside. Two of the students prefer to work in Mumbai while three prefer to work outside. In how many ways assignment
  13. Fish tank
    zebra_fish A fish tank at a pet store has 8 zebra fish. In how many different ways can George choose 2 zebra fish to buy?
  14. Hockey
    hokej Hockey match ended 8:2. How many different matches could be?
  15. Calculation of CN
    color_combinations Calculate: ?
  16. First class
    prvni_jakost The shipment contains 40 items. 36 are first grade, 4 are defective. How many ways can select 5 items, so that it is no more than one defective?
  17. The confectionery
    ice_cream The confectionery sold 5 kinds of ice cream. In how many ways can I buy 3 kinds if order of ice creams does not matter?