Question

In how many ways three different rings can be worn in four fingers with at most one in each finger?

• A. 24
• B. 12
• C. 36
• D. 120

Answer 1

The correct option is A 24

Since we cannot wear more than one ring in any finger means repetition is not allowed.
Hence, the first ring can be worn in any of the available 4 fingers in 4 ways and the second ring can be worn in any of the remaining 3 fingers in 3 ways and the third ring can be worn in any of the remaining 2 fingers in 2 ways.
So the required number of ways in which all the 3 rings can be worn in 4 fingers $=4\times 3\times 2=24$
Alternatively: We have 4 places to be filled up with 3 different things (i.e., rings), which can be done in ${}^4{P}_3$ ways. ${}^4{P}_3=24$