Question

if nPr = 6720 and nCr=56 find n and r​

Answer 1

n = 8  & r = 5  if nPr = 6720 and nCr=56

Step-by-step explanation:

replacing r with x

ⁿPₓ  = 6720 => n!/(n - x)!   = 6720

nCₓ  = 56  => n!/x!(n - x)!   =56

on dividing

x! = 6720/56

=> x! = 120

=> x! = 5!

=> x = 5

=> r = 5

n!/(n - x)!   = 6720

=> n!/(n - 5)! = 6720

=> n(n-1)(n-1)(n-3)(n-4) = 6720

on Hit & Trial method

n = 8

n = 8  & r = 5

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Answer 2

Three steps solutions

Step-by-step explanation:

According to the questions,

$n_p__r$ = 6720

$\frac{n!}{(n - r)!} = 6720$ ..........(1)

$\frac{n!}{(n - r)!\times r!} = 56$ ..................(2}

Solve the above equation simultaneously,

n! = n!

$(n - r)! \times 6720 = (n - r)!\times r! \times 56$

$r! = \frac{6720}{56}$

r! = 120

or,

r = 5

Again solve the above equations,

$\frac{n!}{(n - r)!} = 6720$

put the value of r,

then,

$\frac{n!}{(n - 5)!} = 6720$

$\frac{n\times (n - 1)\times (n - 2)\times (n - 3)\times (n - 4)\times (n -5)!}{(n -5)!} = 6720$

n = 8