How many different two- digit numbers can be formed using each of the digits 3, 5, and 7 only once ?
To find out the number of different two-digit numbers that can be formed using the digits 3, 5, and 7 only once, we can use the concept of permutations.
A permutation is an arrangement of objects in a specific order. In this case, we want to find the number of ways we can arrange the digits 3, 5, and 7 to form two-digit numbers, where each digit is used only once.
Since we're looking for a two-digit number, we need to consider the ones place and the tens place.
To form a two-digit number, we have two choices for the tens place (since it cannot be zero), and once we choose the tens place digit, we have two choices left for the ones place.
Let's break it down step by step:
Step 1: Choose the digit for the tens place. We have three options (3, 5, and 7).
Step 2: After choosing the digit for the tens place, we have two options remaining for the ones place.
Step 3: Multiply the number of options for each step. In this case, 3 (options for the tens place) multiplied by 2 (options for the ones place) equals 6.
Therefore, there are six different two-digit numbers that can be formed using the digits 3, 5, and 7 only once.