Consider the cases of show 1 and then show 2 and then show 3
For show one he has ____ x _____ (8 tricks to pick first then 7 for his second trick (so the two tricks are not the same).
Then we ADD on case 2 where her performs 2 more tricks. Now at show two he wants the exact same first number as in show 1
so
_____ x _____
becomes 1 (for the exact first number from show 1) then ____ (but his second number can not be any of the 7 he used as trick 2 in the first show)
so ____ x _____ becomes 1 x6
So for shows 1 and 2 we have
8x7 + 1x6
with this logic can you generate the third show?
a magician has a repertoire of 8 magic tricks of which he performs 2 on each show. In how many ways can he plan his program for 3 successive shows if:
he does not want to perform the same trick on any 2 successive shows?
He wants to use the same trick for the opening trick of each show?
Can you please show me how to set it up?
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