Question

If nc9 =nc8, find nc2

Answer 1

Method (1):

From,

» nC9 = nC8

we get, 9 + 8 = n

» n = 17

Now,

» nC2 = 17 × 8 = 136

______________________________

Method (2):

» nC9 = nC8

» (n - 8)/9 = 1

» n = 17

Substitute n = 17 in

» nC2 = 17C2 = 136

Hence, nC2 = 136 is the required answer.

Answer 2

Answer:

ⁿc2 = 136

Step-by-step explanation:

Given: nс8 = nс8

To find:  nс2

Solution: Here we use combination  .

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

ⁿCr =        n!       ,ⁿCr = number of combinations ,

          r!(n-r)!         n = total number of objects in the set, r = number of choosing objects from the set.

ⁿC9 =      n!               and ⁿC8 =     n!    

         9!(n-9)!                             8!(n-8)!

Then as given      n!       =      n!      

                           9!(n-9)!       8!(n-8)!

                    ( n-8)!   =    9!

                      (n-9)!          8!

                  (n-8)(n-8-1)!  = 9(9-1)!

                     (n-9)!                8!

                 (n-8)(n-9)!  = 9×8!

                   (n-9)!             8!

⇒ n-8 = 9

⇒n = 9+8 = 17

Now, ⁿс2 =    n!      

                  n!(n-2)!

putting n= 17,we get

ⁿс2 =   17!       = 17(17-1)(17-2)! = 17×16       (since n!=n(n-1)(n-2)! ,and

         2!(17-2)!        2!(17-2)!          1×2                        2! = 2×1)

∴ ⁿc2 = 17×8 = 136

#SPJ3