12 minutes
Arrangement Possibilities Explained
The problem asks us to determine the total time required to arrange four distinct puzzle books on a shelf in every possible order. We are given that each unique arrangement takes 30 seconds to complete.
Permutations Calculation for Arrangements
To find out how many different ways the four books can be arranged, we need to calculate the number of permutations of these four books. The formula for permutations of 'n' distinct items is \(n!\) (n factorial).
In this case, we have 4 books, so \(n=4\). The total number of possible arrangements is:
\(4! = 4 \times 3 \times 2 \times 1\)
Calculating this value:
\(4! = 24\)
This means there are 24 different ways to arrange the four puzzle books on the shelf.
Time Calculation for All Arrangements
We know that each of these 24 arrangements takes 30 seconds. To find the total time, we multiply the number of arrangements by the time taken for each arrangement.
Total Time (in seconds) = Number of Arrangements \(\times\) Time per Arrangement
\(\text{Total Time} = 24 \times 30 \text{ seconds}\)
\(\text{Total Time} = 720 \text{ seconds}\)
Conversion to Minutes
The question asks for the time in minutes. Since there are 60 seconds in one minute, we need to convert the total time from seconds to minutes.
Total Time (in minutes) = Total Time (in seconds) \(\div\) 60
\(\text{Total Time} = \frac{720 \text{ seconds}}{60 \text{ seconds/minute}}\)
\(\text{Total Time} = 12 \text{ minutes}\)
Therefore, it will take 12 minutes to arrange all four puzzle books in every possible order.
Similar Questions
- A player holds 15 cards of four suits, of which eight are red and seven are black. The number of diamonds is twice the number of spades, and the number of hearts is equal to the number of diamonds. How many clubs does he hold?
- In how many ways can 5 people be seated in a row such that A and B are not next to each other?
- In how many ways can 6 people be seated around a round table?
- If 6 people are seated at a round table, how many distinct seating arrangements are possible?
- In a row of 8 seats, how many ways can 3 people sit next to each other?
- In a row of 8 seats, how many ways can 3 people sit next to each other?
- If 3 men and 2 women are seated in a row, how many seating arrangements are possible such that no woman is seated next to
another woman? - How many ways can 4 people be seated in a circle if two people must sit next to each other?
Important Questions from Permutation and Combination
On a chess board, in how many different ways can 6 consecutive squares be chosen on the diagonals along a straight path ?
There are 6 persons arranged in a row. Another person has to shake hands with 3 of them so that he should not shake hands with two consecutive persons. In how many distinct possible combinations can the handshakes take place ?
In a tournament of Chess having 150 entrants, a player is eliminated whenever he loses a match. It is given that no match results in a tie/draw. How many matches are played in the entire tournament?
The letters A, B, C, D and E are arranged in such a way that there are exactly two letters between A and E. How many such arrangements are possible?
There is a numeric lock which has a 3-digit PIN. The PIN contains digits 1 to 7. There is no repetition of digits. The digits in the PIN from left to right are in decreasing order. Any two digits in the PIN differ by at least 2. How many maximum attempts does one need to find out the PIN with certainty?
