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If the hats are indistinguishable, how many ways are there to distribute all five hats among eleven people so that no one gets more than one hat?

Answer :

462 ways are there to distribute all five hats among all eleven people so that no one gets more than one hat

given that

In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations). For example, given three fruits, say an apple, an orange and a pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange. More formally, a k-combination of a set S is a subset of k distinct elements of S. So, two combinations are identical if and only if each combination has the same members. (The arrangement of the members in each set does not matter.) If the set has n elements, the number of k-combinations, denoted as nck

there are 5 hats

there are 11 people

now , we need to distribute all five hats among all eleven people so that no one gets more than one hat = 11 [tex]C_{5}[/tex]

= [tex]\frac{11!}{5!(11-5)!}[/tex]

=462 combinations

462 ways are there to distribute all five hats among all eleven people so that no one gets more than one hat

To learn more about combinations:

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