2nd class combinations

From how many elements you can create 4560 combinations of the second class?

Correct result:

n =  96

Solution:

(n2)=n(n1)2=4560;n>0 n2n9120=0  a=1;b=1;c=9120 D=b24ac=1241(9120)=36481 D>0  n1,2=b±D2a=1±364812 n1,2=1±1912 n1,2=0.5±95.5 n1=96 n2=95   Factored form of the equation:  (n96)(n+95)=0   n>0n=96{{ n} \choose 2} = \dfrac{n(n-1)}{2}=4560;n>0 \ \\ n^2 -n -9120 =0 \ \\ \ \\ a=1; b=-1; c=-9120 \ \\ D = b^2 - 4ac = 1^2 - 4\cdot 1 \cdot (-9120) = 36481 \ \\ D>0 \ \\ \ \\ n_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 1 \pm \sqrt{ 36481 } }{ 2 } \ \\ n_{1,2} = \dfrac{ 1 \pm 191 }{ 2 } \ \\ n_{1,2} = 0.5 \pm 95.5 \ \\ n_{1} = 96 \ \\ n_{2} = -95 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (n -96) (n +95) = 0 \ \\ \ \\ \ \\ n>0 \Rightarrow n=96



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
Looking for help with calculating roots of a quadratic equation?
Would you like to compute count of combinations?

You need to know the following knowledge to solve this word math problem:

Next similar math problems:

  • Combinations
    math_2 From how many elements we can create 990 combinations 2nd class without repeating?
  • Combinations
    trezor_1 How many elements can form six times more combinations fourth class than combination of the second class?
  • 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?
  • Trinity
    trojka How many different triads can be selected from the group 43 students?
  • 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?
  • Menu
    jedalnicek On the menu are 12 kinds of meal. How many ways can we choose four different meals into the daily menu?
  • 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
  • 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?
  • Hockey
    hokej Hockey match ended 8:2. How many different matches could be?
  • Disco
    vencek On the disco goes 12 boys and 15 girls. In how many ways can we select four dancing couples?
  • 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 assignmen
  • Equation
    calculator_2 Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
  • Calculation of CN
    color_combinations Calculate: ?
  • A book
    books_32 A book contains 524 pages. If it is known that a person will select any one page between the pages numbered 125 and 384, find the probability of choosing the page numbered 252 or 253.
  • Discriminant
    Quadratic_equation_discriminant Determine the discriminant of the equation: ?
  • Roots
    parabola Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
  • Quadratic equation
    kvadrat_2 Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.