A panel of six experts is to present opposing arguments in a discussion of legal

Question

A panel of six experts is to present opposing arguments in a discussion of legalizing marijuana for medical purposes. The three proponents arrive first and decide to sit in such a way that the panelists will alternate pro and con. In how many ways can all six panelists be seated if they adhere to the same seating rules?

The gift-wrap desk at a large department store offers 4 box sizes, 9 wrapping papers, 7 colors of ribbon in three widths, and 5 special items to be added to the bow. How many different ways are there to gift-wrap a package if the customer must choose a box, but need not choose any of the other offerings?

Explanation / Answer

Solution:

( a )

total number of experts = 6

number of pros = 3

number of cons = 3

first there are two choses for the pros to select i.e.,, whether they take first position or second position

then there will be 3 members of pros with 3 seats available to take which gives 3! ways

and then there will be 3 members of cons with 3 seats available to take which gives 3! ways

=> tatal number of ways six expers can take seat = 2 * 3! * 3! =2 * 6 * 6 = 72 ways

( b )

number of boxes = 4

number of wrapping papers = 7

number of ribbons =7

number of special items = 5

total number of different ways there to gift-wrap a package if the customer must choose a box = 4 * 9 = 36 ways

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