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Q:  A bag contains club, heart, spade, star, and circle. How many different sets of 4...

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thi-dallas | Student, Undergraduate | Valedictorian

Posted April 29, 2013 at 7:55 PM via web

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Q:  A bag contains club, heart, spade, star, and circle. How many different sets of 4 of these can be formed into?

 

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted April 30, 2013 at 3:53 AM (Answer #2)

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There are 5 different types of items in the bag. These are clubs , hearts, spades, stars and circles. The number of different sets of 4 items that can be formed has to be determined. This problem does not involve merely determining the number of combinations of 4 items from a set of 5 items as there is no restriction on whether repetition is allowed. Any type of item can be included more than once in the set that is being formed.

If r items are being chosen from a set containing n items and  repetition is allowed, the total number of sets that can be formed is given by the formula `((n+r-1)!)/(r!*(n-1)!)`

From the information given, n = 5 and r = 4. This gives the number of sets that can be created as: `((5+4-1)!)/(4!*(4-1)!)` = `(8!)/(4!*4!)` = 70.

70 different sets can be created of 4 items taken from bag containing clubs, hearts, spades, stars and circles.

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