A team of size m has to be chosen from a group of n people (m< n) and a captain chosen for the team.
(a) How many ways can the captained team bechosen if the captain is chosen first then the remainder of theteam chosen.
(b) How many ways can the captained team bechosen if the team is chosen first then the captain chosen from theteam? This should give the same number as a) but a differentformula.
give a justification of answers pls (set notation,bijection principal, addition or multiplication theorem, cartesianproduct etc...)
(c) If n = 4 and m = 3 draw the selection treefor each of (a) and (b). Be sure to carefully label the nodes ofthe tree with the corresponding subsets and the branches of thetree with the corresponding choices.
(d) For the selection tree you draw in (c)write down the element of [4] × [3] that each path in the selectiontree maps to using the bijection discussed in lectures. That is,write the 2-tuple at the end of each of the selection paths of theselection tree.
DO PART C & D ONLY!!! with formulas from part a andb should be 12 ways
