I am not getting the derivation of the formula nPr=n!÷(n-r)!. n=no. of objects and r=no. of times taken (the object)

Question

riya · Answer

Please answer it fast! not able to understand permutations and combinations without it. 😢 Anyone kindly answer it. Hurry up please!!

Ajay · Answer

Consider that you have three drawers and 10 balls of different colors. Now in how many ways can you fill all three drawers with balls from set of 10 balls so that each drawer conatins one ball. Here n = 10 and r =3. 1 st drawers can have any of 10 balls Second drawer can have any of remaining 9 balls Third drawer can have any of the 8 remaining balls. Hence Total Number of ways = 10*9*8 = (10*9*8* 7!)/7! = 10!/(10-3)! Now for us n = 10 and r =3, hence the formula becomes clear

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I am not getting the derivation of the formula nPr=n!÷(n-r)!. n=no. of objects and r=no. of times taken (the object)

I am not getting the derivation of the formula nPr=n!÷(n-r)!.
n=no. of objects and r=no. of times taken (the object)

2 Answers

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I am not getting the derivation of the formula nPr=n!÷(n-r)!. n=no. of objects and r=no. of times taken (the object)

I am not getting the derivation of the formula nPr=n!÷(n-r)!.n=no. of objects and r=no. of times taken (the object)

2 Answers

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I am not getting the derivation of the formula nPr=n!÷(n-r)!.
n=no. of objects and r=no. of times taken (the object)