find r if 16p(15,r)=13p(16,r)
please solve this
Answers
Answer:
For this problem, I will use the simplest way possible to solve this.
Step-by-step explanation:
Remember that:
n Pr = n!(
n
−
r
)
!
For
6
P
r
=
30
, we have:
6
!
(
6
−
r
)
!
=
30
⇒
720
(
6
−
r
)
!
=
30
1
Using the fact that
a
⋅
b
c
⋅
b
=
a
c
, we can see that:
720
(
6
−
r
)
!
=
30
1
720
⋅
x
(
6
−
r
)
!
⋅
x
=
30
1
Where
x
=
30
720
⇒
1
24
Therefore,
720
⋅
1
24
(
6
−
r
)
!
⋅
1
24
=
30
1
Which means that
(
6
−
r
)
!
⋅
1
24
=
1
. We try to simplify this equation.
(
6
−
r
)
!
=
24
Now, we try to think of our basic factorial numbers.
1
!
=
1
2
!
=
2
3
!
=
6
4
!
=
24
Oh!
6
−
r
must equal 4...!
We can now solve the equation:
6
−
r
=
4
−
r
=
−
2
r
=
2
Given : 16. P (15 , r) = 13. P ( 16 , r)
To Find : r
Solution:
P ( n , r) = n !/(n - r)!
16. P (15 , r) = 13. P ( 16 , r)
=> 16, 15!/ (15 - r)! = 13. 16! / (16 - r)!
16. 15 ! = 16 !
=> 16! / (15 - r )! = 13. 16! / (16 - r )!
=> (16 - r )! = 13 * ( 15 - r )!
This is only possible
=> 13! = 13 * 12!
=> 16 - r = 13 and 15 - r = 12
=> r = 3
Hence Value of r is 3
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