Question

if nc6=nc5 find n and nc2​

Answer 1

Solution

verified

Given

n

C

8

=

n

C

6

⇒

8!(n−8)!

n!

=

6!(n−6)!

n!

⇒

8.7

1

=

(n−6)(n−7)

1

⇒ (n−6)(n−7)=56

⇒ n

2

−13n−14=0

⇒ n=−1 or 14

n cannot be (−)ve, ∴ n=14

Now

n

C

2

=

2!×12!

14!

=

2

14×13

=7×13=91

Answer 2

Answer:

The value of     n = 11

The value of nc₂ = 55

Step-by-step explanation:

Formula of ncₓ:

• The formula of ncₓ is used to find the number of ways where x objects are chosen from n objects where the order is not important.
• It is represented in the form of

                 ncₓ = n!/[x!(n-x)!]

        Given,      

                           nc₆ = nc₅

                     $\frac{n!}{6!(n-6)!}=\frac{n!}{5!(n-5)!}$

                      5!(n-5)! = 6!(n-6)!

           5!×(n-5)×(n-6)! = 6×5!×(n-6)!

                             n-5 = 6

                                n = 6+5

                                n = 11

        Foe n = 11,

                          nc₂ = 11c₂ = (11!)/2!(11-2)!

                                           = (11!)/2!×9!

                                           = (11×10×9!)/2!×9!

                                            = 11×10/2

                                            = 11×5

                                            = 55

    Hence, the value of n = 11 and

                 the value of nc₂ = 55

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