Solutions from a student (dragged) 19

Solutions from a student (dragged) 19 - k-1 committee...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Problem 10 (committee’s with a chair) Part (a): We can select a committee with k members in ± n k ² ways. Selecting a chairper- son from the k committee members gives k ± n k ² possible choices. Part (b): If we choose the non chairperson members Frst this can be done in ± n k - 1 ² ways. We then choose the chairperson based on the remaining n - k +1people. Combining these two we have ( n - k +1) ± n k - 1 ² possible choices. Part (c): We can Frst pick the chair of our committee in n ways and then pick
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: k-1 committee members in ± n-1 k-1 ² . Combining the two we have n ± n-1 k-1 ² , possible choices. Part (d): Since all expressions count the same thing they must be equal and we have k ± n k ² = ( n-k + 1) ± n k-1 ² = n ± n-1 k-1 ² . Part (e): We have k ± n k ² = k n ! ( n-k )! k ! = n ! ( n-k )!( k-1)! = n !( n-k + 1) ( n-k + 1)!( k-1)! = ( n-k + 1) ± n k-1 ²...
View Full Document

This note was uploaded on 02/25/2011 for the course STAT 418 taught by Professor G.jogeshbabu during the Winter '08 term at Pennsylvania State University, University Park.

Ask a homework question - tutors are online