Math logic

There are 20 children in the group, each two children have a different name. Alena and John are among them. How many ways can we choose 8 children to be among the selected

A) was John
B) was John and Alena
C) at least one was Alena, John
D) maximum one was Alena, John?

Result

a =  50388
b =  18564
c =  75582
d =  196035840

Solution:

p1=7!=5040 a=1 19 18 17 16 15 14 13/p1=1 19 18 17 16 15 14 13/5040=50388p_{ 1 } = 7! = 5040 \ \\ a = 1 \cdot \ 19 \cdot \ 18 \cdot \ 17 \cdot \ 16 \cdot \ 15 \cdot \ 14 \cdot \ 13/p_{ 1 } = 1 \cdot \ 19 \cdot \ 18 \cdot \ 17 \cdot \ 16 \cdot \ 15 \cdot \ 14 \cdot \ 13/5040 = 50388
p2=6 5 4 3 2 1=720 b=1 1 18 17 16 15 14 13/p2=1 1 18 17 16 15 14 13/720=18564p_{ 2 } = 6 \cdot \ 5 \cdot \ 4 \cdot \ 3 \cdot \ 2 \cdot \ 1 = 720 \ \\ b = 1 \cdot \ 1 \cdot \ 18 \cdot \ 17 \cdot \ 16 \cdot \ 15 \cdot \ 14 \cdot \ 13/p_{ 2 } = 1 \cdot \ 1 \cdot \ 18 \cdot \ 17 \cdot \ 16 \cdot \ 15 \cdot \ 14 \cdot \ 13/720 = 18564
p3=7 6 5 4 3 2 1 2=10080 c=3 19 18 17 16 15 14 13/p3=3 19 18 17 16 15 14 13/10080=75582p_{ 3 } = 7 \cdot \ 6 \cdot \ 5 \cdot \ 4 \cdot \ 3 \cdot \ 2 \cdot \ 1 \cdot \ 2 = 10080 \ \\ c = 3 \cdot \ 19 \cdot \ 18 \cdot \ 17 \cdot \ 16 \cdot \ 15 \cdot \ 14 \cdot \ 13/p_{ 3 } = 3 \cdot \ 19 \cdot \ 18 \cdot \ 17 \cdot \ 16 \cdot \ 15 \cdot \ 14 \cdot \ 13/10080 = 75582
d=2 17 16 15 14 13 12 11=196035840=1.960358108d = 2 \cdot \ 17 \cdot \ 16 \cdot \ 15 \cdot \ 14 \cdot \ 13 \cdot \ 12 \cdot \ 11 = 196035840 = 1.960358\cdot 10^{ 8 }



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
Would you like to compute count of combinations?

Next similar math problems:

  1. Blocks
    cubes3_1 There are 9 interactive basic building blocks of an organization. How many two-blocks combinations are there?
  2. Count of triangles
    SquareTriangle Given a square ABCD and on each side 8 internal points. Determine the number of triangles with vertices at these points.
  3. Confectionery
    cukrovinky The village markets have 5 kinds of sweets, one weighs 31 grams. How many different ways a customer can buy 1.519 kg sweets.
  4. Weekly service
    school_table.JPG In the class are 20 pupils. How many opportunities have the teacher if he wants choose two pupils randomly who will weeklies?
  5. Chords
    chords How many 4-tones chords (chord = at the same time sounding different tones) is possible to play within 7 tones?
  6. 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?
  7. Committees
    globe How many different committees of 6 people can be formed from a class of 30 students?
  8. Menu
    jedalnicek On the menu are 12 kinds of meal. How many ways can we choose four different meals into the daily menu?
  9. Hockey
    hokej Hockey match ended 8:2. How many different matches could be?
  10. Calculation of CN
    color_combinations Calculate: ?
  11. Examination
    examination The class is 21 students. How many ways can choose two to examination?
  12. Commitee
    committees A class consists of 6 males and 7 females. How many committees of 7 are possible if the committee must consist of 2 males and 5 females?
  13. 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?
  14. PIN - codes
    pin How many five-digit PIN - code can we create using the even numbers?
  15. Big factorial
    sierpinski How many zeros end number 116! ?
  16. 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 qu
  17. Median
    statistics The number of missed hours was recorded in 11 pupils: 5,12,6,8,10,7,5,110,2,5,6. Determine the median.