A team of size m has to be chosen from a group of n people (m...

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 be chosen if the captain is chosen first then the remainder of the team chosen.

(b) How many ways can the captained team be chosen if the team is chosen first then the captain chosen from the team? This should give the same number as a) but a different formula.

give a justification of answers pls (set notation, bijection principal, addition or multiplication theorem, cartesian product etc...)

(c) If n = 4 and m = 3 draw the selection tree for each of (a) and (b). Be sure to carefully label the nodes of the tree with the corresponding subsets and the branches of the tree 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 selection tree maps to using the bijection discussed in lectures. That is, write the 2-tuple at the end of each of the selection paths of the selection tree.

DO PART C & D ONLY!!! with formulas from part a and b should be 12 ways

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Expert Solution

Colby Messinger answered 1 year ago

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