SOLUTION: Prove that 6C2 + 6C3 = 7C3 Step 1 6! 6! --- + --- 2!4! 3!3! Step 2 6! 4*6! ---- + ----- 4*3!3! 4*3!3! Step 3 5*6!

SOLUTION: Prove that 6C2 + 6C3 = 7C3 Step 1 6! 6! --- + --- 2!4! 3!3! Step 2 6! 46! ---- + ----- 43!3! 43!3! Step 3 56!

Question 939432: Prove that 6C2 + 6C3 = 7C3
Step 1 6! 6!
--- + ---
2!4! 3!3!
Step 2 6! 4*6!
---- + -----
4*3!3! 4*3!3!
Step 3 5*6!
------
4*3!3!
Step 4 7! 7*6!
---- = -----
3!4! 4*3!3!
Step 5 5*6! 7*6!
----- not equal -----
4*3!3! 4*3!3!
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!

Prove that 6C2 + 6C3 = 7C3

That is prove that

        6!         6!         7!
     -------- + -------- = --------
     2!(6-2)!   3!(6-3)!   3!(7-3)!         

which simplifies to:

          6!    6!     7!
         --- + ---- = ----
         2!4!  3!3!   3!4!


Step 1    6!    6! 
         --- + ---- 
         2!4!  3!3! 

Your first fraction is wrong on step 2. You needed a
3 factor to make the 2! into a 3!

Step 2    6!   4*6!               3*6!       4*6!
        ---- + ----- should be --------  +  -----
       4*3!3!  4*3!3!          3*2!4*3!     4*3!3! 

Step 3                            3*6!       4*6!     
                               --------  +  -----
                                  3!4!       4!3!

Step 4                            3*6! + 4*6! 
                                 -------------
                                     3!4!
                                
Step 5                               7*6!
                                    ------
                                     3!4!

Step 6                                7! 
                                    ------
                                     3!4!

Edwin

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