Combination and Permutation questions

  • Thread starter yc716
  • Start date
  • #1
2
0
Hi,
Can anyone help me with these permutation/combination questions?

Solve the equation for n:
1. nC4 = 35
2. nC4 = 70

It would be really good if I got the answers with full explanations, a.s.a.p. Thanks.
 
Last edited:

Answers and Replies

  • #2
matt grime
Science Advisor
Homework Helper
9,395
3
THere is nothing wrong with trial and error some times.

nCr is increasing (for a fixed r)

Alternatively write nC4=35 out in factorials and get a 4th order polynomial to solve.

You can improve this since it is the same as n(n-1)(n-2)(n-3)=35*24

so n is very close to the 4th root of 35*24
 
  • #3
solve(n*(n-1)*(n-2)*(n-3)=35*24,n); -4, 7, 3/2 + 1/2 I sqrt(111), cc.

solve(n*(n-1)*(n-2)*(n-3)=70*24,n); -5, 8, 3/2 + 1/2 I sqrt(159), cc

I cannot remember the formula for quartic polynomials. Just look up in Abramowich or use Maple.
 
Last edited:
  • #4
HallsofIvy
Science Advisor
Homework Helper
41,833
956
Since n must be an integer, it's easier to use "trial and error". In particular 6C4= [itex]\frac{(6)(5)}{(2)}[/itex]= 15 which is too small while 7C4= [itex]\frac{(7)(6)(5)}{(3)(2)}[/itex]= 35. Aha!

8C4= [itex]\frac{(8)(7)(6)(5)}{(4)(3)(2)}[/itex]= 70.
 
  • #5
Hi,
Can anyone help me with these permutation/combination questions?

Solve the equation for n:
1. nC4 = 35
2. nC4 = 70

It would be really good if I got the answers with full explanations, a.s.a.p. Thanks.
yes
nC4=n!/4!.(n-4)!=n(n-1)(n-2)(n-3)[(n-4)!]/(n-4)!.24=35
now n(n-1)(n-2)(n-3)=35*24
n(n-1)(n-2)(n-3)=7*6*5*4
compairing both sides we gwt
n=7
n-1=6 so n=7
ans n=7
 
  • #6
matt grime
Science Advisor
Homework Helper
9,395
3
This thread is 3.5 years old, doubt that it's going to be of interest to the OP now.
 
  • #7
HallsofIvy
Science Advisor
Homework Helper
41,833
956
I wondered why I didn't recognize my own response!
 

Related Threads on Combination and Permutation questions

Replies
2
Views
2K
  • Last Post
2
Replies
28
Views
2K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
14
Views
8K
Replies
3
Views
6K
Replies
4
Views
884
  • Last Post
Replies
5
Views
780
Replies
3
Views
1K
Replies
2
Views
3K
Replies
6
Views
752
Top