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What is nAr nCr and nPr?

Updated: 12/17/2022
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Q: What is nAr nCr and nPr?
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What is a general equation that expresses the relationship between permuation nPr and combination nCr?

nCr = nPr/r!


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The combination formula is usually written as nCr representing the number of combinations of r objects at a time taken from n. nCr = n!/[r!*(n-r)!] The permutation formula is usually written as nPr representing the number of permutations of r objects at a time taken from n. nPr = n!/r! Where n! [n factorial] is 1*2*3*....*(n-1)*n


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I am not stupid enough to try and list them since there are 55*54*53*52*51*50/(6*5*4*3*2*1) = 28,989,675 combinations. nPr=permutation while nCr=combination. The question is how many combination of 6 are there in 55 numbers. So the answer should be based on the formula: nPr = n!/(n-r)! where ! is factorial and nCr = nPr/r! = n!/{(n-r)*r!} ; So using the formula should look likr this 55C6 = 55!/{(55-6)!*6!} = 55!/(49!*6!) = 28,989,675


Difference between nCr and nPr?

you use nPr, when you want to take note of the order. Example, in choosing between A,B,C,D & E , how many ways can you choose any 3 arranged letters. (This means ABC is different from ACB or BCA or...) Then 5P3. you use nCr , when the order is not important. Example , how many ways can you get three letters from A,B,C,D & E. (here ABC is no different from BAC since you just got A&B&C.) Then 5C3. I got this from yahoo answers :P


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