3. Spider has one sock and one shoe for each of its 8 legs.in how many different ways can the spider put on its socks and shoes, assuming that in each leg the sock has to be put on before the shoe.
(8!)^2/2
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You can put all 8 socks on first for 8! ways and then all 8! shoes on next for 8! more ways. This is not the only possibility, so the lower bound is 8!. You can choose all 16 in a random fashion, but some combinations would violate the rules, so the upper bound is 16!. C & E are the lower and upper bounds, so the answer is in between them, 16!
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