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1. ### Let n and k be any positive integers with k less than or equal to n. Prove C (n, k )= C (n,n- k ).?

C (n,n - k ) = n!/((n - k )! (n - (n - k ))!) = n!/((n - k )! (n - n + k )!) = n!/((n - k )! k !) = C (n, k )

2 Answers · Science & Mathematics · 14/01/2012

2. ### hi, can somebody help me find all the values of k for which:?

in this kind of equation C =Co and k is a constant that has to be solved using dif e with values that you have not given. im pretty sure on that.

1 Answers · Science & Mathematics · 05/06/2010

3. ### Show that if A->B (arrow labeled f) and B-> C (arrow labeled k ) are isomorphisms,?

... the binary operation on A or on B as appropriate. And since k :B→ C is an homomorphism, k ( f(x) ) + k ( f(y) ) = k ( f(x + y) ), that is, ( k ...

1 Answers · Science & Mathematics · 14/12/2008

4. ### Prove: C (n, k ) = C (n, n- k ). using theorem C (n, k ) = n! / { k !(n- k )!}?

C (n, k ) = n! / {( k !)(n- k )!} C (n,n- k ) = n! / {(n- k )!(n-(n- k ))!} = n! / {(n- k )!( k !)} C (n,n- k ) = C (n, k )

2 Answers · Science & Mathematics · 23/10/2007

5. ### Help with this math question Solve for R?

C = K * (Rr)/(R+r) C (R+r) = KRr CR + Cr = KRr CR - KRr = -Cr R( C - Kr) = -Cr R = -Cr / ( C - Kr)

1 Answers · Science & Mathematics · 18/09/2013

6. ### Prove (n+1) C k = n C k -1 +n C k . A question in combinatorics?

nCr / nC(r-1) = (n-r+1)/r nCk = n!/(n- k )! k ! nC( k -1) = n!/(n- k +1)!( k -1)! nC( k -1) = nCk * k /(n...

1 Answers · Science & Mathematics · 03/08/2008

7. ### Given a =2i -4j- k c =3i + j -2k find (a. c ) (axc) ?

I am assuming that i,j, k represent a 3 d system and therefore a and b are vectors a = {2, -4, -1}; c = {3, 1, -2}; and a. c is the Dot Product then a. c = 4

2 Answers · Science & Mathematics · 11/11/2013

8. ### Let p be prime and 1 <= k < p. Prove that p divides the binomial coefficient C (p, k )?

C (p, k ) = p! / k ! (p- k )!. So C (p, k ) k ! (p- k )! = p!. Consider the unique factorization in prime numbers of C (p, k ) k ! (p- k )! = p!. The prime factors of C (p, k ) k ! (p- k ...

4 Answers · Science & Mathematics · 18/09/2007

9. ### k2 + 3k + 2 = (k2 + k ) + 2 ( __________ )?

k ^2 + 3k + 2 = k ^2 + (1 + 2) k + 2 = k ^2 + k + 2k + 2 =( k ^2 + k )+ 2 ( k + 1)

1 Answers · Science & Mathematics · 09/07/2015

10. ### Evaluate lim{n- ∞} Σ[ k =0,n] C (n+ k ,n) x^n (1-x)^ k ?

...distribution ok .. . .. . last correction! the density function is f( k ; r,p) = C ( k +r-1, r-1) p^r (1 - p)^ k Note: C ( k +r-1, k ) = C ( k +r-1...

1 Answers · Science & Mathematics · 26/08/2008