Question

How many 2 – digit numbers can be formed from the digits {1, 2, 3, 4, 5} without repetition and with repetition?

Answer 1

Hint: In the above question we have to form 2 – digit numbers from the given, so we will use the concept of arrangement of numbers.

Complete step-by-step answer:
Here in the above question we can get the number of ways to form 2 – digit numbers from the given set by using Permutation. We have 5 digits and we need to choose 2 digits.

Then the number of 2 – digit numbers formed from the given set without repetition is
\[{}^{5}{{P}_{2}}=\dfrac{5!}{\left( 5-2 \right)!}=\dfrac{5!}{3!}=20\]

The numbers that can be formed by repetition are {11, 22, 33, 44, 55}.

So, there are a total 5 numbers that can be formed by repetition.

\[\therefore \] The number of 2 – digit number formed from the given set with repetition,
\[={}^{5}{{P}_{2}}+5=20+5=25\]

Therefore, the total number of 2 – digit numbers that can be formed by the given digits

without repetition are 20 and with repetition are 25.

Note: Just remember the concept of Permutation which is an arrangement of all or part of a set of objects, with regard to the order of the arrangement. Also remember that this is the difference between combination and permutation, most of you don’t know about it. In permutation we care about the order of the elements, whereas the combination we don’t.