SOLUTION: Compute each of the following. Look for simplifications first.
a. 20P15 (the 20 and the 15 are small)It's looking for the permutation??
b. (n+1)!
------
(n-1)!
T
Algebra.Com
Question 246255: Compute each of the following. Look for simplifications first.
a. 20P15 (the 20 and the 15 are small)It's looking for the permutation??
b. (n+1)!
------
(n-1)!
Thank you so much in advance.
This is so difficult.
~Marney
Found 2 solutions by jim_thompson5910, TheProdicalSon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
a)
Start with the given formula
Plug in and
Subtract to get 5
Expand 20!
Expand 5!
Cancel
Simplify
Now multiply 20*19*18*17*16*15*14*13*12*11*10*9*8*7*6 to get 20,274,183,401,472,000
================================================================
b)
!}{(n-1)!})
... Start with the given expression.
(n+1-1)(n+1-2)(n+1-3)(n+1-4)\cdots(3)(2)(1)}{(n-1)!})
... Expand the numerator. Remember that n! = n(n-1)(n-2)(n-3)...(3)(2)(1). So (n+1)! = (n+1)(n+1-1)(n+1-2)(n+1-3)(n+1-4)...(3)(2)(1)
(n)(n-1)(n-2)(n-3)\cdots(3)(2)(1)}{(n-1)!})
... Combine like terms.
(n)(n-1)!}{(n-1)!})
... Take note that (n-1)! = (n-1)(n-2)(n-3)...(3)(2)(1) which is what the numerator (minus the first two terms) looks like. So rewrite (n-1)(n-2)(n-3)...(3)(2)(1) as (n-1)!
Note: if you're asking 'Why did we just do that?' The goal is to cancel out the factorials. Since the denominator has a (n-1)! term, we just need that term in the numerator for it to cancel out.
(n))
... Cancel out the common terms.
)
... Rearrange the terms.
... Distribute
So !}{(n-1)!}=n^2+n)
where 'n' is an integer and
Answer by TheProdicalSon(34) (Show Source): You can put this solution on YOUR website!
The first one is pretty simple.
20P15 = 20(amount to choose from)permutation 15(amount needed)
this is written as which translates into (after simplification)
20 * 19 * 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6
= 20,274,183,401,472,000
The second one.
I have no idea, I believe the answer is already as simplified as it can get
but I really don't know, sorry.
Comment on my page if this was helpful.
Sincerely,
TheProdicalSon
RELATED QUESTIONS
(n+1)!
------
(n-2)!
The directions say: Compute each of the following. Look for... (answered by jsmallt9)
There is one more that I can't get.
Roll a pair of dice 20 times and count the number... (answered by venugopalramana)
According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s... (answered by ikleyn)
Find the exact value using a sum or difference identity. Some simplifications may involve (answered by ikleyn)
Two dice are rolled 20 times. Compute Pe(13), the empirical probability of obtaining a... (answered by venugopalramana)
Sylvia buys a small farm (a quarter section of 160 acres) for $225 000.00. She makes a... (answered by solver91311)
I+(I+2)(3) THere are 9 fewer math books than English books. Write an expression for the... (answered by checkley71)
Consider the following problem. Mike and Tim are looking to earn a little extra money.... (answered by jorel1380)
An important factor in selling a residential property is the number of people who look... (answered by stanbon)