Question

on an alien planet every alien has 6 legs. jack, one of the aliens, living there has one sock and one shoe for each of his 6 legs. in how many different orders can he put on his socks and shoes, assuming that on each leg, the sock must be put on before the shoe?

Answer 1

To determine the number of different orders Jack can put on his socks and shoes, given that he must put on the sock before the shoe for each of his 6 legs, we can use permutations.

Permutations are used when the order of arranging objects matters. In this case, there are 6 legs, and for each leg, Jack has to put on a sock and then a shoe. So, we have 2 actions (putting on a sock and putting on a shoe) for each leg.

The total number of permutations is calculated as 2 * 2 * 2 * 2 * 2 * 2, where each "2" represents the two possible orders (sock first or shoe first) for each leg.

2 * 2 * 2 * 2 * 2 * 2 = 2^6 = 64

So, there are 64 different orders in which Jack can put on his socks and shoes for his 6 legs, following the rule that the sock must be put on before the shoe for each leg.