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!

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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