Soup is on sale when you buy 5 cans at a time, which you have decided to do. You

Question

Soup is on sale when you buy 5 cans at a time, which you have decided to do. You arrive early enough so that there are over 5 cans of each of the 12 kinds of soup on the shelves. (All dented cans, etc. have been removed, so swapping one can of soup for another of the same kind – e.g. swapping one can of chicken soup for another can of chicken soup – makes no difference.) 99. How many ways could you select 5 different kinds of soup? 100. How many ways could you select 5 different kinds of soup, given that one of your selections will be corn chowder? 101. How many ways could you select 5 kinds of soup, given that you will select exactly two cans of corn chowder, but the remaining ones of different kinds? 102. How many ways could you select 5 cans of soup, if you require yourself to select two cans of the same kind, and three of a different kind (i.e. 4 different kinds)? 103. How many ways could you select 5 cans of soup, if you permit, but do not require, yourself to select two cans of the same kind, and three of a different kind (i.e. 4 or 5 different kinds)?

Explanation / Answer

99. No of ways in which 5 different kind of soups can be selected = 12C5 = 792

100. No of ways in which 5 soups can be selected given than one soup is corn chowder = 1x 11C4 = 330

101. No of ways in which 5 soups can be selected when 2 are corn chowder = 1 x 1 x 11C3 = 165

102. No of ways in which 5 soups can be selected where 2 of a kind is there in the selection = 12C4 x 4 = 1980

103. No of ways in which 5 soups can be selected where there are 4 or 5 different kinds of soups = 12C4 x 4 + 12C5 = 2772

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