Question

Series question help. *attached below* Will give medal.

Answer 1

Can I have some assistance with number 1 of this question, please?

Answer 2

does C stand for choosing

Answer 3

nCr = n! / ( (n-r) ! r ! )

Answer 4

Yes, it does @perl

Answer 5

so we are given
[(x-2) C 2] = 5/2 * [ 4 C 3]

Answer 6

(x-2)! / ( (x -2 -2 )! 2! ) = 5/2 * 4

any questions so far

Answer 7

Hmm, I am lost with the RHS of the equation

Answer 8

4 c 3 = 4! / ( (4-3)! * 3 !

Answer 9

Oh, now I get it.

Answer 10

So the RHS is equal to 10?

Answer 11

yes

Answer 12

How do I proceed now?

Answer 13

so far we have
[(x-2) C 2] = 5/2 * [ 4 C 3]

(x-2)! / ( (x -2 -2 )! 2! ) = 5/2 * 4

(x-2)! / ( (x -4 )! 2! ) = 10

Answer 14

yes

Answer 15

Do you agree that
(x-2)! = (x-2) ( x-3) (x-4)(x-5) ... 3*2*1

Answer 16

by definition
n! = n * (n-1) (n-2) ... * 3 * 2 * 1

Answer 17

Yes, I understand that bit

Answer 18

ok so we will do a trick

(x-2)!
= (x-2) ( x-3) (x-4)(x-5) ... 3*2*1
= (x-2)(x-3)* (x-4)!

Answer 19

[(x-2) C 2] = 5/2 * [ 4 C 3]

(x-2)! / ( (x -2 -2 )! 2! ) = 5/2 * 4

(x-2)! / ( (x -4 )! 2! ) = 10

[(x-2)(x-3)(x-4)!] / ( (x-4)! 2! ) = 10

Answer 20

now you can cancel (x-4)! from the left side

Answer 21

Got the answer now, thanks! :)