The Professor's Response

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

See the professor's answer below.

Hi Natalia,

It does not matter how much you cancel or which specific choices you make while cancelling. For example, in the video I gave you some specific ways you could continue the cancelling. However, you must perform the cancelling correctly. Cancelling is not an operation in mathematics, it is actually division. If you are going to cancel you need to divide properly. If you did not get the same answer as me, you did not divide properly during your cancelling.

You wrote above that you divided 6 into 49 and got 8. You might have made a typo there, but 6 does not divide into 49 evenly. You would need to divide 6 into 48 to get 8. Also, where is your 48 in the calculation? You mentioned cancelling the 47!, 49, 50, 51, and the 52. You include the 53 in the calculation, but where is your 48?

I think all you did wrong was actually leave out your 49 (you must have divided the 48 by 6 to get 8). If you multiply your answer by the missing 49, you get the correct answer.

Hope that helps,

Professor McGuckian