Question

In a party, every person does a "Wakanda Forever" sign with every other person. If there were in total of 210 "Wakanda Forever" done at the party. Find the number of persons present in the party.​

Answer 1

The number of persons present in the party = 21

Given:

In a party, every person does a "Wakanda Forever" sign with every other person

There were in total of 210 "Wakanda Forever" done at the party

To find:

The number of persons present in the party.​

Solution:

Let n be the number of persons in party

According to Permutations and Combinations  

If there are n persons present in a party and every person does a "Wakanda Forever" sign with every other person.

Then, total number of "Wakanda Forever" done at the party will be equals to ⁿC₂

⇒  ⁿC₂ = n(n-1)/2

From given data total number of "Wakanda Forever" done = 210

⇒  n(n-1)/2 = 210

⇒  n(n-1) = 420

⇒  n²- n - 420 = 0  

Now factorize n²- n - 420 = 0  to get n value

⇒  n²- n - 420 = 0  

⇒  n² + 20n - 21n - 420 = 0

⇒  n(n+20) -21(n+20) = 0

⇒ (n+20) (n-21) = 0

⇒ n+20 = 0   and   n - 21 = 0

⇒ n = -20      and   n = 21

Here, n value can't be negative

Therefore we will take n value as 21  

The number of persons present in the party = 21

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Answer 2

Answer:

there are 21 people in the party

Step-by-step explanation:

it is given that there is party and every person in the part does the Wakanda forever sign with every other person .

there were around two hundred and ten Wakanda forever done in the party

to find the number of people

first let us assume that there are n number of people in the party

let total number of Wakanda forever be equals to ⁿC₂

according to the formula

$nC2 = n(n-1)/2$

there were two hundred and ten Wakanda forever done in the party

$n(n-1)/2 = 210\\ n(n-1) = 420\\n2- n - 420 = 0$

$n2- n - 420 = 0 \\n2 + 20n - 21n - 420 = 0\\ n(n+20) -21(n+20) = 0\\(n+20) (n-21) = 0\\n+20 = 0 and n - 21 = 0$

hence the total number of people were 21

this is the concept of permutation and combination

A permutation is an act of arranging objects or numbers in order.

Combinations are the way of selecting objects or numbers from a group of objects or collections, in such a way that the order of the objects does not matter.

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