SOLUTION: If nPr = 336 and nCr = 56, find n and r. Please note that: P and C are permutation and combination respectively.

Algebra.Com
Question 1163219: If nPr = 336 and nCr = 56, find n and r.
Please note that:
P and C are permutation and combination respectively.
Found 3 solutions by ikleyn, solver91311, MathTherapy:
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.

The ratio of these quantities,  nPr and nCr, is  n*(n-1)* . . . *(n-r+1) :   and equals to r!;


so,  r! =  = 6.


Hence, r = 3.


Next,  nPr at r = 3 is  n*(n-1)*(n-2) = 336.


After several simple trials and errors you get  n = 8.


You may also use  (n-1) ~  = 6.95 (approx.)


ANSWER.  n = 8,  r = 3.

Solved.



Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!




and



Hence







336 divided by 8 is 42. Then 6 and 7 are factors of 42. So the numerator of nPr is 8 X 7 X 6, and then the denominator must be 5! and 8 - 3 is 5, so




John

My calculator said it, I believe it, that settles it
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
If nPr = 336 and nCr = 56, find n and r.
Please note that:
P and C are permutation and combination respectively. 



 ------ Substituting for   
 ------ Cross-multiplying
 
, since 3(2)(1) = 6

With r = 3, we can say that: 

This means that there are 3 CONSECUTIVE, DESCENDING INTEGER-FACTORS of 336. These are: 8, 6, and 7

Therefore, we get:

RELATED QUESTIONS

NPR = 336 and ncr = 56 Find r and... (answered by fractalier)
If nPr = 336 and nCr = 56, determine what n and r are. (answered by fcabanski)
ncr=220 and npr=1320 find n and... (answered by edjones)
given nPr=3024 and nCr=126 find n and... (answered by ikleyn,greenestamps)
Please help me to solve this Qeustion(1) Prove that nCr=n+1Cr-nCr-1 and Qeustion (2)... (answered by math_helper)
If nPr= 55400 and nCr=462, determine... (answered by richard1234)
If nPr=55440 and nCr=462nCr =462,determine "\"r\"" (answered by jim_thompson5910)
We Are Given That nPr=3024 and nCr=126.What Will be the Value Of... (answered by stanbon)
Show that nPr = nPr+1 (show that n permutation r equals to n permutation... (answered by mathmate)