Question 1164353: One of the solved problems on this site under lessons of Combination is:
The Quality Assurance Service of a company has to test a sample of 8 tires selected from among 100 tires. In how many ways 8 tires can be selected for testing from this set of 100 tires?
How far I got:
I punched in the following in my TI calculator:
100!/(8!92!)
I got overflow error. The solution is given under the problem which I understand very well. I also know the calculators cannot DISPLAY factorials of above 70. Nevertheless, the calculators can handle the calculations far beyound 70! internally and as long as the answer is within the capability of its display, they will show the results...at least from what I believe.
Yet the problem is so easy to calculate by hand and still not calculator.
What gives? I just want to understand. Please help.
Thanks
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source):
Answer by ikleyn(52780)  (Show Source):
You can put this solution on YOUR website! .
Thanks for stopping and asking this question.
Yes, the binomial coefficient  is equal to  .
But nobody in healthy mind calculates it by calculating 100! as the product of 100 integer factors.
Yes, 100! = 1*2*3*4*. . . *100,
but there is 92! in the denominator 92! = 1*2*3*4*...*92.
So, 92 factors in the numerator and denominator CANCEL each other, leaving VERY SIMPLE formula
for the binomial coefficient =  ,
and there is NO ANY PROBLEM to calculate it manually (which people never do, again), or using TECHNOLOGY (a pocket calculator,
an Excel spreadsheet, an Excel compact standard formula, or online free of charge calculators in numerous Internet web-sites).
Finally, we live in XXI century, and the year is 2020 now . . .
It is my answer to your question.
Everything that I told you in this post, relates to very basics of rational calculations, and it is ASSUMED
that the person wanting calculate binomial coefficients, is familiar with it . . .
Your final statement is "Yet the problem is so easy to calculate by hand and still not calculator."
The value of the binomial coefficient is = 186087894300,
and you say it is so easy to calculate it by hand and still not with a calculator?
It is very interesting to me - how you will do this challenge . . . . Try it and then tell me . . . Ha-ha-ha.
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If you still have questions, I will be more than happy answer them and to be in help (!)
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