Question

2. On the Canadian Senate there are 105 members, 58 are Conservative and 47 are Liberal.

a) How many ways are there to select at least 2 Liberals for a sub-committee of 5 Senate members?

b) What is the probability of selecting 5 people for a sub-committee that contains 1 Liberals and 4 Conservatives?

c) What is the probability that no Liberals are selected in a sub-committee of 5 Senate members?

d) Suppose the 5 members in the sub-committee have rankings of President, Vice-President, Operations Officer, Press Secretary, and Treasurer. What is the probability of selecting all Liberals to these positions

Thanks! due tomorrow as well.

Answer 1

a) number of ways =P(at least 2 liberals)=N(2 liberal and 3 Conservative )+N(3 liberal and 2 Conservative )+N(4 liberal and 1 Conservative )+N(5 liberal and 0 Conservative )

=⁴⁷C₂*⁵⁸C₃ +⁴⁷C₃*⁵⁸C₂ +⁴⁷C₄*⁵⁸C₁ +⁴⁷C₅*⁵⁸C₀ =72037840

b) probability of selecting 5 people for a sub-committee that contains 1 Liberals and 4 Conservatives

=⁴⁷C₁*⁵⁸C₄ /¹⁰⁵C₅ =47*424270/96560646 =0.206509

c)

probability that no Liberals are selected in a sub-committee of 5 Senate members= ⁴⁷C₀*⁵⁸C₅ /¹⁰⁵C₅

=1*4582116/96560646 =0.047453

d)

probability of selecting all Liberals to these positions =⁴⁷C₅ /¹⁰⁵C₅ =1533939/96560646 =0.015886