# Counting and Combinations

2 Questions

QUESTION 1 of 2

Prof. I am having same issue on #40 ch 3 Probability

It says find 10C2 on calculator answer is 45. But if I attempt to work it out this is what I get:
1st try: (10/2)= 10!/2! Then I get 10*9*8*7*6*5*4*3*2!/2! I cancel both 2!'s so am left with 10*9*8*7*6*5*4*3=1,814,400. Can you explain please. I know I got right answer using calculator but this simplifying is driving me crazy! Not sure what am doing wrong.

QUESTION 2 of 2

Prof. I have a question on Basic Probability - Combination Rule Problem # 39
I did the steps 53C6 = (53 / 6) = 53!/6! 47! Then I understand getting =53*52*51*50*49*48*47!/6*5*4*3*2*1 47!

From here you say we can cancel, on your video you only cancelled some numbers... This is where am confused. I try to do the problems or finish them before so I want to know if what I did is wrong & why?
I cancelled 6 into the 49 =8 5 into the 50=10 3 into 51= 17 2 into 52=26 & 47! into 47!

This left me with 53*26*17*10*8 / 4*1 = 1874080/4 = 468,520

Is this answer incorrect? I now how you got, 22,957,480, I got same answer using the calculator & the nCr function but I would like to understand if I did anything wrong by simplifying more & if I did, then how do you know how much to simplify (saying we don't have a calculator). BTW I do understand the video. But just have that confusion with the simplifying. Thank you