In how many ways can seven beads of distinct colors be put on the hexagonal grid shown, if reflections and rotations of an arrangement are considered equivalent?

Second one -----

A row of 8 light switches controls different banks of lights in a school gymnasium. In preparation for a school dance, students decide that they want either one or two banks of lights on during the dance. How many possible ways are there of setting these 8 switches so that either one or two banks of lights are on?

Maplesnowy
Feb 23, 2018

#1**+1 **

7 ways to chosse the middle one

Put another down anywhere

5! ways to order the rest

So that is 840

that takes care of rotation but not relfections

There are six axes of symmetry so I'll have to divide by something...not sure what.

2 of the places are fixed before the other 5 get included so maybe there is only really one reflection that counts.

So maybe

840/2 = 420 But that is a bit of a guess but is seems right .... well maybe anyway.

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I do not understand the second question - I do not know what is being asked.

Melody
Feb 23, 2018

#3**+1 **

I THINK the second question is as follows

each switch controls one bank , so there is EIGHT ways to have ONE bank on

then for TWO banks there is 8 C 2 ways = 28 ways

28+8 = 36 ways to have either one bank or two banks on,

~EP

ElectricPavlov
Feb 23, 2018