could any one work this out for me and show the work. i need it really badly....
problem: 31C25 X 15C10 / 46C35
PLEASE HELP ME!!!!!
2007-08-30 10:45:08 · 6 answers · asked by johnsondonavon 1 in Science & Mathematics ➔ Mathematics
N choose K is n! / (n-k)! k!
31 C 25 = 736281
15 C 10 = 3003
46 C 35 = 13340783196
Doing the number crunching...
(736281 * 3003) / 13340783196 = 0.165736
2007-08-30 11:07:59 · answer #1 · answered by PMP 5 · 0⤊ 0⤋
31C25 could mean How many ways can you pick 25 objects out of 31 (without replacement) if the order does not matter.
It is also written 31P25 (31, pick 25) or C(31, 25). You also see it written inside a pair of tall brackets, with the 31 above the 25 -- looks like a fraction without the bar in the middle.
The formula is
C(31, 25) = 31! / (25! * (31-25)!)
where ! means factorial (31! is the product of all the numbers from 1 to 31).
You can note that
31! / 25! = 31*30*29*28*27*26
(all the numbers from 1 to 25 cancel out)
So you are left with
31*30*29*28*27*26 / (1*2*3*4*5*6)
My calculator gives
C(31, 25) = 736,281
C(15,10) = 15! / [ 10! * (15-10)!]
C(15,10) = 15*14*13*12*11 / (1*2*3*4*5)
C(15,10) = 30,030
C(46, 35) = 46! / [ 35! * (46-35)!)
C(46, 35) = 46! / ( 35! * 11!)
C(46, 35) = 46*45*44*...*37*36 / (1*2*...*10*11)
C(46, 35) = 39,916,800
That was the long (but easy) way.
At this point, you can perform the calculation.
-------
The "shorter" way is to write the formulas in one equation:
[ 31! / (25!*6!)] * [ 15! / (10!*5!)] / [ 46! / (35!*11!)]
[ 31! / (25!*6!)] * [ 15! / (10!*5!)] * [ (35!*11!) / 46!]
(31! * 15! * 35! * 11! ) / ( 25! * 6! * 10! * 5! * 46!)
A scientific calculator or a computer spreadsheet should be able to give you the answer 0.1657363...
---
However, if you are doing this by hand: it is long but it is possible. Mathematicians were doing these routinely in the early 1700's.
"cancel out", pairing factorials that are closest in value. For example:
46! / 35! = 46*45*...*37*36 (note that 35 has been cancelled out)
11! / 10! = 11
31! / 25! = 31*30*29*28*27*26
15! / 6! = 15*14*...*8*7
(and we are left with 5! in the denominator, not paired with anyone).
(31! * 15! * 35! * 11! ) / ( 25! * 6! * 10! * 5! * 46!)
becomes
31*30*29*28*27*26 * 15*14*13*12*11*10*9*8*7 * 11
divided by
46*45*44*43*42*41*40*39*38*37*36 * 5*4*3*2*1
You can continue to cancel out (for example, 11 goes into 44 four times) and calculate whatever is left.
-----
2007-08-30 17:53:43 · answer #2 · answered by Raymond 7 · 0⤊ 0⤋
Oh My, I have it figured by I dont think I can show my math here .... It's really simple. If you work it out, I know you will be able to see the same thing as I. Good Luck anyway.
2007-08-30 17:51:22 · answer #3 · answered by Charley 5 · 0⤊ 0⤋
well i tried finding the answer on my calculator...
I'm assuming that your Cs mean nCr or the Combinations function
31 nCr 25 = 736281
15 nCr 10 = 3003
736281 * 3003 = 221104884
221104884 / (46 nCr 35) = .1657
hopefully that is what you're looking for
2007-08-30 17:54:38 · answer #4 · answered by odonata 2 · 0⤊ 0⤋
are you solving for C??? what the heck does 31C25 mean??? is that like 31 times 25 times C??
2007-08-30 17:51:00 · answer #5 · answered by mighty_power7 7 · 0⤊ 0⤋
Uh, are letters suppose to be involved in math? and why?
2007-08-30 17:49:07 · answer #6 · answered by Anonymous · 1⤊ 0⤋