Asked by kelley
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?
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?
Answers
Answered by
MsPi_3.14159265
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?
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?
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