The magician, The Great Ziginy, is planning his next world tour. He knows a total of 7 different illusions but he only has time to perform 4 of them at any show. The Great Ziggy does not want any two of his shows to be identical, so they cannot contain the same 4 illusions in the same order. What is the most number of cities The Great Ziggy can visit and perform at on his tour?+
7^4=2401, that's the answer
wrong....the correct answer is 840
C(7,4) = 7*6*5*4 = 840
C(7,4)=35*4!=840
AS No of ways he can select 4 out of 7 is 35 and each he can arrange in different order in 4! ways.
To determine the maximum number of cities The Great Ziggy can visit and perform at on his tour, we need to consider the number of unique combinations of 4 illusions that he can perform out of the 7 illusions he knows.
The formula to calculate the number of combinations is given by nCr = n! / r!(n-r)!, where n is the total number of items and r is the number of items to be chosen.
In this case, n is 7 (the total number of illusions) and r is 4 (the number of illusions to be chosen for each show).
Using the formula, we can calculate the number of combinations:
7C4 = 7! / 4!(7-4)!
= 7! / 4!3!
= (7 * 6 * 5 * 4!) / (4! * 3 * 2 * 1)
= 7 * 6 * 5 / (3 * 2 * 1)
= 35
So The Great Ziggy can perform 35 unique combinations of 4 illusions.
Now, to determine the maximum number of cities he can visit, we need to consider that each show cannot contain the same 4 illusions in the same order. This means that once The Great Ziggy performs a particular combination of 4 illusions, he cannot repeat it again in subsequent shows.
Since he has 35 unique combinations, he can perform 35 different shows in 35 different cities. Therefore, the maximum number of cities The Great Ziggy can visit and perform at on his tour is 35.