# Combinations

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

Correct result:

n =  45

#### Solution:

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

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

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

## Next similar math problems:

• 2nd class combinations
From how many elements you can create 4560 combinations of the second class?
• Combinations
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?
• Combinations
How many elements can form six times more combinations fourth class than combination of the second class?
• Variations 3rd class
From how many elements we can create 13,800 variations 3rd class without repeating?
• 2nd class variations
From how many elements you can create 2450 variations of the second class?
• Variations 4/2
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.
• Combinations 6
6 purses 9 flaps 12 straps Every combination must include 1 purse, 1 flap, and 1 strap. How many are possible combinations?
• Two-element combinations
Write all two-element combinations from elements a, b, c, d.
• Class pairs
In a class of 34 students, including 14 boys and 20 girls. How many couples (heterosexual, boy-girl) we can create? By what formula?
• VCP equation
Solve the following equation with variations, combinations and permutations: 4 V(2,x)-3 C(2,x+ 1) - x P(2) = 0
• Elements
If the number of elements is decreased by two the number of permutations is decreased 30 times. How many elements are?
• Statistics
The sum of all deviations from the arithmetic mean of the numerical sequence 4, 6, 51, 77, 90, 93, 95, 109, 113, 117 is:
• Family
94 boys are born per 100 girls. Determine the probability that there are two boys in a randomly selected family with three children.
• I think number
I think number.When I add 841 to it and subtract 157, I get a number that is 22 greater than 996. What number I thinking?
• Party
At the party everyone clink with everyone. Together, they clink 406 times. How many people were at the party?
• Variations
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.
• Permutations without repetition
From how many elements, we can create 720 permutations without repetition?