Question

In how many ways can 5 keys be put in a ring?

Answer 1

the key can be put in ring in 120 ways

Answer 2

Heya!!


Let the keys be A, B, C, D, E

The number of ways of putting 5 different keys in a ring is very similar to that of arranging in a row except.

ABCDE and EABCD are the same combinations when placed in a ring.

For all the keys to be arranged in a row the number of arrangements is 5!=120

Now,
Lets select some random arrangement:- ADECB

For this arrangement the other arrangements which make the same arrangement when arranged in a ring are:-

=> BADEC

=> CBADE

=> ECBAD

=> DECBA

=> ADECB (the initial one)

Therefore, there are groups of 5 arrangements which mean the same thing when arranged in a ring so we can happily divide the total number of arrangemengts in a row by 5

So,

=> 120/5=24

Therefore,
The answer is 24.