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1. ### CHALLENGE: Prove that Σ k * C[M,k] * C[(N-M),(n-k)] / C[N,n] = M*n/N?

...black is given by the well-known hyper-geometric formula: P(k) = C[M,k] * C[(N-M),(n-k)] / C[N,n], /numerator...

1 Answers · Science & Mathematics · 05/09/2007

2. ### Is the total differential of delta m= K/C equal to (k / c^2) - (1/c) or is it (c-k) / c^2 ?

If m = k/c If k is a constant, then Δm = (-k/c²)Δc If k is not a constant, then Δm = (-k/c²)Δc + (1/c)Δk

1 Answers · Science & Mathematics · 04/12/2008

3. ### Prove that ∑k*C(n, k) = n2^(n - 1)?

...1 Now put x = 1 and you will get ......................n n*(2)^(n - 1) = ∑ k * C(n,k) ...................k=1

3 Answers · Science & Mathematics · 24/11/2009

4. ### Prove that C(n,k) = C(n,n-k)?

Take the expression n-k and put in in place of k. C(a, b) means take the formula for C(n, k), use a in place of n and b...

2 Answers · Science & Mathematics · 05/05/2014

5. ### Prove discrete math identity C(n,r)⋅C(r,k) = C(n,k)⋅C(n-k,r-k)?

... X. This corresponds to the product C(n,k)⋅C(n-k,r-k). Every such pair of subsets A,B is...

4 Answers · Science & Mathematics · 27/07/2013

6. ### 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

7. ### How to plot function in matlab or maple for example {(F/M)/(k-c)^2+ω^2}*{exp(-kt) – exp(-ct)*[cosωt-{(k-c)/(ω)

t = t_start:h:t_end; y = {(F/M)/(k-c)^2+ω^2}*{exp(-k*.t) – exp(-c*t)*[cosω*.t-{(k-c)/(ω) ; plot(t,y); (t_start, t...

1 Answers · Science & Mathematics · 08/11/2007

8. ### What is the value of k + c if f(x) is everywhere differentiable. ?

...28 + c c = 6k - 10 12k = 28 + 6k - 10 6k = 18 k = 3 c = 6(3) - 10 c = 8 k + c = 3 + 8 = 11

1 Answers · Science & Mathematics · 11/01/2009

9. ### If k = abc + 1, then prove that (k,a) = (k,b) = (k,c) = 1?

I'm afraid I don't understand the notation. What do the quantities in parentheses represent? ---- (k,a), (k,b) & (k,c)

1 Answers · Science & Mathematics · 25/01/2012

10. ### 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