Two wizards try to create a spell using all the four elements, water, air, fire, and earth. For this, they decide to mix all these elements in all possible orders. They also decide to work independently. After trying all possible combination of elements, they conclude that the spell does not work.
How many attempts does each wizard make before coming to this conclusion, independently?
Calculating Wizard Spell Attempts
The problem asks for the number of ways four distinct elements (water, air, fire, earth) can be arranged in different orders.
This is a permutation problem, as the order of elements matters, and all elements are distinct.
The number of ways to arrange n distinct items is calculated using the factorial function, denoted as n!.
In this case, there are 4 distinct elements (n=4).
The calculation is as follows:
$ n! = 4! $
$ 4! = 4 \times 3 \times 2 \times 1 $
$ 4! = 24 $
Therefore, each wizard makes 24 attempts independently before concluding that the spell does not work.
Important Questions from Permutations and Combinations
A police station has six personnel comprising an inspector (I) and five constables ($C_1, C_2, C_3, C_4, C_5$). Normally, a 'raid team' of two, three, or four members is formed depending upon the nature of the raid. As per rule, it is mandatory that the inspector is part of raid team.
Number of distinct raid teams that can be formed is __________________.
(Answer in integer)
Five teams have to compete in a league, with every team playing every other team exactly once, before going to the next round. How many matches will have to be held to complete the league round of matches?
- How many 4-digit positive integers divisible by 3 can be formed using only the digits {1, 3, 4, 6, 7}, such that no digit appears more than once in a number?
- How many five-digit numbers can be formed using the integers 3, 4, 5 and 6 with exactly one digit appearing twice?
- Mixed species flocks of birds include social and solitary species. There are 5 social species and 10 solitary species in a forest. Flocks always have a total of 5 species, of which 2 are social and 3 are solitary. The number of types of flocks with unique species composition is ________.(Answer in integer)
