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