Question

if npr=504 and ncr=84 find n and r

Answer 1

the value of r is equals to 3 . and the value of n will be equal to 9.

Answer 2

Answer:

The value of r = 3 and n = 9.

Step-by-step explanation:

Permutation (nPr) is the arrangement of elements in order. Combination (nCr) is the process of selecting the elements from a collection of distinct items, considering the order of selection is not disturbed.

Given,

nPr = 504

nCr = 84

Permutation is formulated as -

nPr = $\frac{n!}{(n-r)!}$

Combination is formulated as -

nCr = $\frac{n!}{(n-r)!r!}$

The relation between permutation and combination can be formulated as follows-

$nCr = \frac{nPr}{r!}$

Therefore, by equating the values we get

$84 = \frac{504}{r!}$

$r! = \frac{504}{84}$

$r!$ = 6

that is, r=3

We know that,

nPr = $\frac{n!}{(n-r)!}$

504 = $\frac{n!}{(n-3)!}$

$\frac{n(n-1)(n-2)(n-3)!}{(n-3)!}$ = 504

n(n-1)(n-2) = 9 × 8 × 7

n = 9.

Therefore, the value of r is 3 and n is 9.