Combinations

From how many elements we can create 990 combinations 2nd class without repeating?

Correct result:

n =  45

Solution:

(n2)=n(n1)2=990;n>0 n2n1980=0  a=1;b=1;c=1980 D=b24ac=1241(1980)=7921 D>0  n1,2=b±D2a=1±79212 n1,2=1±892 n1,2=0.5±44.5 n1=45 n2=44   Factored form of the equation:  (n45)(n+44)=0   n>0n=45{{ n} \choose 2} = \dfrac{n(n-1)}{2}=990;n>0 \ \\ n^2 -n -1980 =0 \ \\ \ \\ a=1; b=-1; c=-1980 \ \\ D = b^2 - 4ac = 1^2 - 4\cdot 1 \cdot (-1980) = 7921 \ \\ D>0 \ \\ \ \\ n_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 1 \pm \sqrt{ 7921 } }{ 2 } \ \\ n_{1,2} = \dfrac{ 1 \pm 89 }{ 2 } \ \\ n_{1,2} = 0.5 \pm 44.5 \ \\ n_{1} = 45 \ \\ n_{2} = -44 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (n -45) (n +44) = 0 \ \\ \ \\ \ \\ n>0 \Rightarrow n=45



We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 0 comments:
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:

  • 2nd class combinations
    color_circle From how many elements you can create 4560 combinations of the second class?
  • Variations 3rd class
    cubic From how many elements we can create 13,800 variations 3rd class without repeating?
  • 2nd class variations
    cards From how many elements you can create 2450 variations of the second class?
  • Combinations
    trezor_1 How many elements can form six times more combinations fourth class than combination of the second class?
  • Combinations
    kvadrat_3 If the number of elements increase by 3, it increases the number of combinations of the second class of these elements 5 times. How many are the elements?
  • Permutations without repetition
    permutations_3 From how many elements we can create 720 permutations without repetition?
  • Variations 4/2
    pantagram_1 Determine the number of items when the count of variations of fourth class without repeating is 600 times larger than the count of variations of second class without repetition.
  • Class pairs
    pair_1 In a class of 34 students, including 14 boys and 20 girls. How many couples (heterosexual, boy-girl) we can create? By what formula?
  • Committees
    globe How many different committees of 2 people can be formed from a class of 21 students?
  • Wagons
    vlak2 We have six wagons, two white, two blue, and two red. We assemble trains from them, wagons of the same color are exactly the same, so if we change only two white wagons on a train, it's still the same train, because I don't know any different. How many di
  • Fruits
    banan_1 In the shop sell 4 kinds of fruits. How many ways can we buy three pieces of fruit?
  • Chocolates
    Chocolate In the market have 3 kinds of chocolates. How many ways can we buy 14 chocolates?
  • Beads
    koralky2 How many ways can we thread 4 red, 5 blue, and 6 yellow beads onto a thread?
  • Honored students
    metals Of the 25 students in the class, 10 are honored. How many ways can we choose 5 students from them, if there are to be exactly two honors between them?
  • Bouquets
    flowers In the flower shop they sell roses, tulips and daffodils. How many different bouquets of 5 flowers can we made?
  • 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?
  • Variations
    pantagram Determine the number of items when the count of variations of fourth class without repeating is 42 times larger than the count of variations of third class without repetition.