How do you find out how many ways the integers 1,2,3,4,5,6,7,8 can be placed in a circle if: at least three odd numbers are together?

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Noemi Flores · Accepted Answer

Step 1Let&#039;s first look at the number of ways we can place three odd numbers together. That&#039;s a permutation question:            P              n        ,        k              =                  n        !                              (          n          -          k          )                !              ;    n    =          population        ,    k    =          picks                  P              4        ,        3              =                  4        !                              (          4          -          3          )                !              =                  4        !                    1        !              =    24  Step 2The rest of the numbers (5) can be placed in any order:            P              5        ,        5              =                  5        !                              (          5          -          5          )                !              =    5    !    =    120  The one other thing we need to remember is that this is a &quot;sitting in a circle&quot; problem - and so unlike sitting in a row (where there is definitely a chair 1 with person A in it, chair 2 with person B, etc), we have to eliminate the duplicate arrangements from simply rotating the table chairs. Since there are 8 people, there are therefore 8 ways to do each arrangement of chairs, and so we divide by 8.In total then, we have:                     24        ×        120            8        =    360

How do you find out how many ways the integers

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