Question

-digit numbers are formed, without replacement, from the digits 5, 6, andlist the elements of sample space for the given experiment two digit numbers are formed without replacement from the digits 5 6 and 7 ​

Answer 1

The sample space for forming two-digit numbers without replacement from the digits 5, 6, and 7 consists of the numbers 56, 57, 65, 67, 75, and 76.

Step-by-step explanation:

The question asks us to list the sample space of two-digit numbers that can be formed without replacement from the digits 5, 6, and 7. Since we are forming two-digit numbers without replacement, each number must consist of two different digits from the set {5, 6, 7}.

To construct the sample space, we consider each digit can be in the tens place, and then we pair it with each of the remaining digits in the ones place. Doing this systematically, we create the following pairs:

• 
  
• 56
• 
  
• 57
• 
  
• 65
• 
  
• 67
• 
  
• 75
• 
  
• 76

This list represents the complete sample space for our experiment of creating two-digit numbers without replacement from the digits 5, 6, and 7.