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  • A person has 5 different keys on their keyring. In how many different ways can they arrange the keys on the keyring, if the order of the keys matters and repetition of keys is allowed?</p

A person has 5 different keys on their keyring. In how many different ways can they arrange the keys on the keyring, if the order of the keys matters and repetition of keys is allowed?

Option: 1

3125


Option: 2

2245


Option: 3

4152


Option: 4

5125


Answers (1)

best_answer

Since repetition of keys is allowed, each key can be placed in any of the 5 positions on the keyring. 

Using the formula for permutation with repetition, the number of arrangements can be calculated as,

\begin{aligned} & N=5^5 \\ & N=5 \times 5 \times 5 \times 5 \times 5 \\ & N=3125 \end{aligned}

Therefore, there are 3125 ways to arrange the keys on the keyring.

 

 

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