There are 15 employees working on a project. The project is successfully approved by the company and the company decided to give the best employee award. In order to give it they have to make comparisons among the 15 members. Find the number of comparisons needed?

Here are some formulas for permutations and combinations:  Permutations: The formula for permutations is nPr = n!/(n-r)! .  Permutations are used for lists of data where the order of the data matters.  Combinations: The formula for combinations is nCr = n!/[r! (n-r)!].  Combinations are used for groups of data where the order of the data doesn't matter.  Number of ways to arrange \(r\) things out of \(n\) different things: The formula is nPr = n! (n−r)! .  Number of ways to select \(r\) things out of \(n\) given things wherein \(r\le n\): The formula is nPr = r!×nCr.  nCn = 1 and nC0 =... Show more

Here are some formulas for permutations and combinations: 

Permutations: The formula for permutations is nPr = n!/(n-r)! . 
Permutations are used for lists of data where the order of the data matters. 

Combinations: The formula for combinations is nCr = n!/[r! (n-r)!]. 
Combinations are used for groups of data where the order of the data doesn't matter. 

Number of ways to arrange \(r\) things out of \(n\) different things: The formula is nPr = n! (n−r)! . 
Number of ways to select \(r\) things out of \(n\) given things wherein \(r\le n\): The formula is nPr = r!×nCr. 
nCn = 1 and nC0 = 1 
nCr = nC. (n - r):  
(n-1)! ways: If 'n' objects are arranged in a circular way and if the clockwise and anti-clockwise arrangement is different. 
C (n+ r -1 ,r) = (n + r -1 )! / r! (n – 1) !:

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