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Sagot :
Combinations and permutations are operations that allow you to determine in how many ways a determined set of numbers/ objects can be selected in subsets/ groups.
The difference is that for Permutations, the order in which the objects can be selected matters, and for Combinations, the order in which the objects are selected doesn't matter.
1) The expression:
[tex]_nP_r[/tex]Indicates a permutation, is the number of permutations of n- objects taken r times.
For the given definitions, the one that corresponds to this expression is a. The number of groups, where order matters, of size "r" that can be formed from a larger group of size "n".
2) The expression:
[tex]_nC_r[/tex]This expression refers to Combinations of n objects when you take a number r at a time, without looking at the order.
For the given definitions, the one that matches this expression is c. The number of groups, where order does not matter, of size 2r" that can be formed from a larger group of size "n".
3) The expression
[tex]n![/tex]Is the factorial number of n objects, indicates the number of possible permutations of the n objects.
For the given definitions, the one that matches the expression is b. The number of possible arrangements of n items.
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