. 7 prizes are to be distributed between 3 people with a guarantee that each person gets at least one prize. Find the number of ways the prizes can be distributed.

Total number of ways to distribute the prize = 2187

Step-by-step explanation:

Given:

Number of prizes = 7

Number of peoples = 3

We need to find the total number of ways to distribute the prize.

Solution:

From the above statement, 7 prizes are to be distributed between 3 people, wherein each person gets at least one prize.

Each prize is to be distributed among three persons. When the first prize is to be awarded, one of the three is chosen to win the prize. When the second prize is to be awarded, there are again three choices.

So, total number of distribution of the prizes is given as:

Therefore, total number of ways to distribute the prizes = 2187

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0