Question

If n*P_{5} = 4!n*C_{6} , what is the value of n​

Answer 1

A

7

B

14

Explanation:

As

n

C

4

,

n

C

5

,

n

C

6

are in A.P., so

n

C

4

+

n

C

6

=

2

n

C

5

⇒

1

+

n

C

6

n

C

4

=

2

×

n

C

5

n

C

4

⇒

1

+

n

!

4

!

(

n

−

4

)

!

n

!

6

!

(

n

−

6

)

!

=

2

×

n

!

4

!

(

n

−

4

)

!

5

!

(

n

−

5

)

!

n

!

⇒

1

+

(

n

−

4

)

(

n

−

5

)

6

×

5

=

2

×

(

n

−

4

)

5

⇒

30

+

n

2

−

9

n

+

20

=

12

n

−

48

⇒

n

2

−

21

n

+

98

=

0

⇒

(

n

−

7

)

(

n

−

14

)

=

0

∴

n

=

7

,

14