Is 10! over 8! equal to 448?

👨🏻‍🏫 學術台 數學
2008-02-14 6:27 am
This is how I solved it:

10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
over
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

Than I canceled 8-1 out, left with 10 x 9 = 90 over 40320
I got 40320 from multiplying:
8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320
so, I than have 90 over 40320, which I than divide these two ( 40320 divided by 90) which is 448.

Is that the correct answer? If not, can you please help me solve it?! Thanks ^_^
更新1:

So, if you cancel the numbers out from both top and bottom of fractions, than you just need to multiply the top and do notthing with the bottom?! Is that correct??

回答 (8)

2008-02-14 10:56 am
✔ 最佳答案
10 ! / 8 ! = (10 x 9 x 8! ) / 8! = 90
👍 3 👎 4
2008-02-14 2:33 pm
No.

10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

Cancel the (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) from both factorials

You are left with

10 * 9 = 90

Add on:
After you have cancelled the common terms (in this case it is from 1 to 8), there is nothing left in the denominator so all you have to do is to multiply the numbers left in the numerator to get the answer.
👍 2 👎 1
2008-02-14 2:31 pm
n! = n(n-1)!
10! = 10×9!
= 10×9×8!

10!/8! = 10×9 = 90
👍 1 👎 1
2008-02-14 2:35 pm
You made two GROSS errors.

One... if you take 40320 and divide that by 90, you do get 448... but why would you do that if its 90 OVER 40320? Your fraction is upside down. You are taking the numerator and dividing it into the denominator... which is bad, misconceived math. Its supposed to be denominator divided into the numerator. Really, this error is a matter of not knowing fractions.

Two... if you canceled 8! out of the denominator, why did you leave it in the numerator? This error is partly a factorial error, and partly an algebraic error of not knowing to reduce fractions.
👍 1 👎 2
2008-02-14 3:14 pm
If you cancel correctly, you should be left with 10 x 9 which is 90.
👍 0 👎 1
2008-02-14 2:40 pm
10 x 9 x 8 x 7 . . . 1 / 8 x 7 x 6 . . . 1 = 90 , cancel 8 x 7 x 6 . . .1 both numerator and denominator thus you have 10 x 9 only so the answer is 90.
參考: statistics book
👍 0 👎 1
2008-02-14 2:31 pm
you do cancel out the 8! from the top and bottom, but that only leaves 10 * 9 = 90.

So 90 is 10! / 8!
👍 0 👎 1
2008-02-14 5:30 pm
(10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)/(8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)
= 3628800/40320
= 90
👍 0 👎 2


收錄日期: 2021-05-01 09:55:10
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