Question

^n Pr *x^nC r then x us equal to __________​

Answer 1

Answer:

When  

r

=

1

,

x

=

n

; When  

r

=

0

,

x

=

1

Explanation:

I think  

x

is the point where we have  

n

P

r

=

n

C

r

so I'll assume that to be the case.

Where we have this relation, we have:

n

!

(

n

−

r

)

!

=

n

!

(

k

!

)

(

n

−

r

)

!

We can divide through by  

n

!

(

n

−

k

)

!

to get to:

1

=

1

r

!

r

!

=

1

⇒

r

=

1

,

0

Does this work?

Let's have a test case of  

n

=

5

,

r

=

1

:

5

!

4

!

=

5

!

(

1

!

)

(

4

!

)

=

5

And now a test case of  

n

=

5

,

r

=

0

:

5

!

5

!

=

5

!

(

5

!

)

(

0

!

)

=

1

And so we end up with 2 cases:

When  

r

=

1

,

x

=

n

When  

r

=

0

,

x

=

1