SOLUTION: what is r if 9Pr= 3024

Question 1083149: what is r if 9Pr= 3024

Found 2 solutions by jim_thompson5910, MathTherapy:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let's compute the following ten nPr values.
Fix n = 9 (ie don't change this value)
Let r be a whole number and let it range from r = 0 to r = 9.
The goal is to find which r value yields n P r = 9 P r = 3024.

-------------------------------------------------------------

When r = 0, then...

n P r = (n!)/((n-r)!)
9 P 0 (9!)/((9-0)!)
9 P 0 = (9!)/(9!)
9 P 0 = (9*8*7*6*5*4*3*2*1)/(9*8*7*6*5*4*3*2*1)
9 P 0 = (362880)/(362880)
9 P 0 = 1

-------------------------------------------------------------

When r = 1, then...

n P r = (n!)/((n-r)!)
9 P 1 (9!)/((9-1)!)
9 P 1 = (9!)/(8!)
9 P 1 = (9*8*7*6*5*4*3*2*1)/(8*7*6*5*4*3*2*1)
9 P 1 = (362880)/(40320)
9 P 1 = 9

-------------------------------------------------------------

When r = 2, then...

n P r = (n!)/((n-r)!)
9 P 2 (9!)/((9-2)!)
9 P 2 = (9!)/(7!)
9 P 2 = (9*8*7*6*5*4*3*2*1)/(7*6*5*4*3*2*1)
9 P 2 = (362880)/(5040)
9 P 2 = 72

-------------------------------------------------------------

When r = 3, then...

n P r = (n!)/((n-r)!)
9 P 3 (9!)/((9-3)!)
9 P 3 = (9!)/(6!)
9 P 3 = (9*8*7*6*5*4*3*2*1)/(6*5*4*3*2*1)
9 P 3 = (362880)/(720)
9 P 3 = 504

-------------------------------------------------------------

When r = 4, then...

n P r = (n!)/((n-r)!)
9 P 4 (9!)/((9-4)!)
9 P 4 = (9!)/(5!)
9 P 4 = (9*8*7*6*5*4*3*2*1)/(5*4*3*2*1)
9 P 4 = (362880)/(120)
9 P 4 = 3024

-------------------------------------------------------------

When r = 5, then...

n P r = (n!)/((n-r)!)
9 P 5 (9!)/((9-5)!)
9 P 5 = (9!)/(4!)
9 P 5 = (9*8*7*6*5*4*3*2*1)/(4*3*2*1)
9 P 5 = (362880)/(24)
9 P 5 = 15120

-------------------------------------------------------------

When r = 6, then...

n P r = (n!)/((n-r)!)
9 P 6 (9!)/((9-6)!)
9 P 6 = (9!)/(3!)
9 P 6 = (9*8*7*6*5*4*3*2*1)/(3*2*1)
9 P 6 = (362880)/(6)
9 P 6 = 60480

-------------------------------------------------------------

When r = 7, then...

n P r = (n!)/((n-r)!)
9 P 7 (9!)/((9-7)!)
9 P 7 = (9!)/(2!)
9 P 7 = (9*8*7*6*5*4*3*2*1)/(2*1)
9 P 7 = (362880)/(2)
9 P 7 = 181440

-------------------------------------------------------------

When r = 8, then...

n P r = (n!)/((n-r)!)
9 P 8 (9!)/((9-8)!)
9 P 8 = (9!)/(1!)
9 P 8 = (9*8*7*6*5*4*3*2*1)/(1)
9 P 8 = (362880)/(1)
9 P 8 = 362880

-------------------------------------------------------------

When r = 9, then...

n P r = (n!)/((n-r)!)
9 P 9 (9!)/((9-9)!)
9 P 9 = (9!)/(0!)
9 P 9 = (9*8*7*6*5*4*3*2*1)/(1)
9 P 9 = (362880)/(1)
9 P 9 = 362880

-------------------------------------------------------------

In the work shown above, we see that 9 P 4 = 3024

So if 9 P r = 3024, then r = 4

-------------------------------------------------------------
-------------------------------------------------------------

Answer: 4
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
what is r if 9Pr= 3024

= n(n - 1)(n - 2).....[n - (r - 1)]

The CONSECUTIVE DECREASING factors of 3,024 are: 9, 8, 7, and 6.
There are 4 (FOUR) decreasing factors, and so: .
Thus,
RELATED QUESTIONS
We Are Given That nPr=3024 and nCr=126.What Will be the Value Of... (answered by stanbon)
given nPr=3024 and nCr=126 find n and... (answered by ikleyn,greenestamps)
Dear math teacher, Would you help me explain how to convert r! to r? Here is the... (answered by jim_thompson5910,MathLover1)
At what rate will rupees 7200 fetch a simple interest of rupees 3024 in 4... (answered by addingup)
If 2^r + 2^r + 2^r + 2^r = 26, what is the value of... (answered by nerdybill,solver91311)
13% if r is 209. What is... (answered by josgarithmetic,ikleyn)
How many ways can the numbers 1,2,3,4,5 be arranged to make a password? Repetition is... (answered by ikleyn)
A line passes through (r,5) and (6,r). If the slope is five eights what is r equal... (answered by ankor@dixie-net.com)