In this case, when the repetition of objects is not allowed, we must be careful, not to choose a specific object more than once. This is the permutation formula for calculating the number of permutations possible for the choice of ‘r’ items from a set of ‘n’ distinct items when repetition is allowed. Using the fundamental principle then, we get, Since this event is taking place ‘r’ times and the act of choosing an item from the available set is always independent of our other choices, we may invoke the Product Rule of Counting here. N(E) = n (the number of ways in which E can take place) Let us call the event of choosing an item as E: So, for choosing ‘r’ items, we have n choices available to us ‘r’ times. When the repetition of items is allowed, at every step of selection from the set of ‘n’ items, we have all the ‘n’ choices available to us since we can make a choice multiple times.
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