There are three different rings to be worn in four fingers with at most one in each finger. In how many ways can this be done?

Options

A. 36
B. 28
C. 24
D. 32

Answer

To solve the problem of how many ways three different rings can be worn on four fingers with at most one ring on each finger, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Elements**: We have 3 different rings (let's call them R1, R2, and R3) and 4 fingers (F1, F2, F3, and F4).

2. **Understand the Constraints**: The problem states that we can wear at most one ring on each finger. This means that we cannot place more than one ring on any single finger.

3. **Choose Fingers for the Rings**: Since we have 3 rings and 4 fingers, we need to choose 3 fingers out of the 4 available fingers to wear the rings. The number of ways to choose 3 fingers from 4 can be calculated using the combination formula:
\[ \text{Number of ways to choose fingers} = \binom{4}{3} = 4 \]
(This means we can choose any 3 fingers from the 4 available fingers.)

4. **Arrange the Rings on the Chosen Fingers**: After selecting which 3 fingers will have rings, we need to arrange the 3 different rings on these 3 fingers. The number of ways to arrange 3 different rings is given by the permutation formula:
\[ \text{Number of arrangements of rings} = 3! = 6 \]

5. **Calculate the Total Ways**: To find the total number of ways to wear the rings, we multiply the number of ways to choose the fingers by the number of arrangements of the rings:
\[ \text{Total ways} = \binom{4}{3} \times 3! = 4 \times 6 = 24 \]

Thus, the total number of ways to wear the three different rings on four fingers is **24**.