At an airshow, 8 skydivers were released from a plane in a circle formation. Each skydiver was connected to each of the other skydivers with a separate pieces of ribbon. How many pieces of ribbon were used in the skydiving act?

The total number of pieces of ribbons that were used in the skydiving act is 28 ribbons

What are Combinations?

The number of ways of selecting r objects from n unlike objects is:

The equation for combination is

ⁿCₓ = n! / ( ( n - x )! x! )

where

n = total number of objects

x = number of choosing objects from the set

Given data ,

The total number of skydivers in the plane n = 8 skydivers

Each  skydiver was connected to each of the other skydivers with a separate pieces of ribbon

So , the number of choosing skydivers x = 2

Now , the total number of ribbons used is calculated by combination

So , the equation is

ⁿCₓ = n! / ( ( n - x )! x! )

Substitute the value of n and x in the equation , we get

⁸C₂ = 8! / ( ( 8 - 2 )! x 2! )

      = 8! / ( 6! x 2! )

      = 8 x 7 / 2 x 1

      = 56 / 2

      = 28 ribbons

Hence , The total number of pieces of ribbons that were used in the skydiving act is 28 ribbons

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Answer:

28

Step-by-step explanation:

If a ribbon connects two skydivers, and there are 8 skydivers total, then we can do 8C2, which is equal to (8*7)/2, which is equal to 28. An alternate solution is to think of it this way. Skydiver 1 is connected to everyone else, which is 7 other people. Skydiver 2 is connected to everyone else but Skydiver 1, which is 6 other people. This goes on until Skydiver 8 is already connected with everyone. So we have 7+6+5+4+3+2+1+0, which is also equal to 28.