10! / 6!(10-6)!=210
My question is, how was this answer arrived at? I can't find factorials on my TI-84 nor can it seem to handle those numbers anyway.
Factorial question (is this enough characters yet?)?
2013-03-18 10:50 pm
回答 (3)
2013-03-18 11:35 pm
✔ 最佳答案
For reference, the factorial symbol ! can be found under [Math] > Prb > 4:!.10! / (6!4!)
= 10 × 9 × 8 × 7 / (4 × 3 × 2 × 1)
= 5040 / 24
= 210
2013-03-19 5:59 am
You don't need a calculator.
Write out the factorials. You get a fraction like this:
10*9*8*7*6*5*4*3*2*1
----------------------------
6*5*4*3*2*1 * 4*3*2*1
The factors 6*5*4*3*2*1 upstairs and downstairs cancel,
and you are left with
10*9*8*7 / 4*3*2*1
8 in the numerator cancels out with 4*2 in the denominator
and you are left with 10*9*7/3 = 10*3*7 = 210.
(In general, n!/m! = n*(n-1)*(n-2)*...*(n-(m-1)), which is easier to calculate.
E.g. 10!/6! = 10*9*8*7)
Write out the factorials. You get a fraction like this:
10*9*8*7*6*5*4*3*2*1
----------------------------
6*5*4*3*2*1 * 4*3*2*1
The factors 6*5*4*3*2*1 upstairs and downstairs cancel,
and you are left with
10*9*8*7 / 4*3*2*1
8 in the numerator cancels out with 4*2 in the denominator
and you are left with 10*9*7/3 = 10*3*7 = 210.
(In general, n!/m! = n*(n-1)*(n-2)*...*(n-(m-1)), which is easier to calculate.
E.g. 10!/6! = 10*9*8*7)
2013-03-19 5:54 am
10!
=
(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)
=
(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)
收錄日期: 2021-04-21 18:07:20
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