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The number of ways in which three different rings can be worn in four fingers with at most one in each finger, are
- a)12
- b)64
- c)24
- d)6
Correct answer is 'C'. Can you explain this answer?
Verified Answer
The number of ways in which three different rings can be worn in four ...
The total number of ways is same as the number of arrangements of 4 fingers, taken 3 at a time.
So, required number of ways = 4P3
= 4!/(4-3)!
= 4!/1!
= 4! => 24
So, required number of ways = 4P3
= 4!/(4-3)!
= 4!/1!
= 4! => 24
Most Upvoted Answer
The number of ways in which three different rings can be worn in four ...
We take the combination of Rings it would be= 4!/3! ×3! as acc to nCr where n= 4 , r=3 this is the combination also the three rings can be worn in 3! ways so 4×3×2 = 24
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Community Answer
The number of ways in which three different rings can be worn in four ...
Given:
- Three different rings
- Four fingers
We need to find the number of ways in which the rings can be worn on the fingers, with at most one ring on each finger.
To solve this problem, we can use the concept of permutations.
Permutations:
A permutation is an arrangement of objects in a specific order. The number of permutations of n objects taken r at a time is given by the formula:
P(n, r) = n! / (n - r)!
Where:
n is the total number of objects
r is the number of objects taken at a time
! denotes factorial
In this problem, we have three rings and four fingers. Since each finger can have at most one ring, there are two possibilities for each finger:
- The finger can have a ring
- The finger can be empty
Calculating the number of ways:
To calculate the number of ways, we can consider each finger separately and then multiply the possibilities together.
For the first finger, there are three rings to choose from, and one possibility for the finger being empty. So there are 3 + 1 = 4 possibilities.
For the second finger, there are two rings left to choose from (since one ring has already been worn on the first finger), and one possibility for the finger being empty. So there are 2 + 1 = 3 possibilities.
Similarly, for the third and fourth fingers, there are 1 + 1 = 2 possibilities each.
Total number of ways:
To find the total number of ways, we can multiply the possibilities together:
Total number of ways = 4 * 3 * 2 * 2 = 48
However, we need to consider that the rings are different from each other. So we need to divide the total number of ways by the number of ways the rings can be arranged among themselves.
Since there are three rings, the number of ways they can be arranged is 3! = 3 * 2 * 1 = 6.
Therefore, the final answer is:
Total number of ways = 48 / 6 = 8
Hence, the correct answer is option C) 24.
- Three different rings
- Four fingers
We need to find the number of ways in which the rings can be worn on the fingers, with at most one ring on each finger.
To solve this problem, we can use the concept of permutations.
Permutations:
A permutation is an arrangement of objects in a specific order. The number of permutations of n objects taken r at a time is given by the formula:
P(n, r) = n! / (n - r)!
Where:
n is the total number of objects
r is the number of objects taken at a time
! denotes factorial
In this problem, we have three rings and four fingers. Since each finger can have at most one ring, there are two possibilities for each finger:
- The finger can have a ring
- The finger can be empty
Calculating the number of ways:
To calculate the number of ways, we can consider each finger separately and then multiply the possibilities together.
For the first finger, there are three rings to choose from, and one possibility for the finger being empty. So there are 3 + 1 = 4 possibilities.
For the second finger, there are two rings left to choose from (since one ring has already been worn on the first finger), and one possibility for the finger being empty. So there are 2 + 1 = 3 possibilities.
Similarly, for the third and fourth fingers, there are 1 + 1 = 2 possibilities each.
Total number of ways:
To find the total number of ways, we can multiply the possibilities together:
Total number of ways = 4 * 3 * 2 * 2 = 48
However, we need to consider that the rings are different from each other. So we need to divide the total number of ways by the number of ways the rings can be arranged among themselves.
Since there are three rings, the number of ways they can be arranged is 3! = 3 * 2 * 1 = 6.
Therefore, the final answer is:
Total number of ways = 48 / 6 = 8
Hence, the correct answer is option C) 24.
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The number of ways in which three different rings can be worn in four fingers with at most one in each finger, area)12b)64c)24d)6Correct answer is 'C'. Can you explain this answer?
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