Question
How many three digits numbers can be formed from the digits 2,5,7,9 . A.If each digit is used once only
B.if each may be used repeatedly
B.if each may be used repeatedly
Answers
GPT 3.5
A. If each digit is used once only:
To form a three-digit number, we have 4 choices for the hundreds digit (2, 5, 7, or 9), 3 choices for the tens digit (the remaining digits after choosing the hundreds digit), and 2 choices for the units digit (the remaining digit after choosing the hundreds and tens digits).
Therefore, the total number of three-digit numbers that can be formed is:
4 choices for the hundreds digit × 3 choices for the tens digit × 2 choices for the units digit = 4 × 3 × 2 = 24.
B. If each digit may be used repeatedly:
To form a three-digit number, we have 4 choices for each of the hundreds, tens, and units digits (2, 5, 7, or 9).
Therefore, the total number of three-digit numbers that can be formed is:
4 choices for the hundreds digit × 4 choices for the tens digit × 4 choices for the units digit = 4 × 4 × 4 = 64.
To form a three-digit number, we have 4 choices for the hundreds digit (2, 5, 7, or 9), 3 choices for the tens digit (the remaining digits after choosing the hundreds digit), and 2 choices for the units digit (the remaining digit after choosing the hundreds and tens digits).
Therefore, the total number of three-digit numbers that can be formed is:
4 choices for the hundreds digit × 3 choices for the tens digit × 2 choices for the units digit = 4 × 3 × 2 = 24.
B. If each digit may be used repeatedly:
To form a three-digit number, we have 4 choices for each of the hundreds, tens, and units digits (2, 5, 7, or 9).
Therefore, the total number of three-digit numbers that can be formed is:
4 choices for the hundreds digit × 4 choices for the tens digit × 4 choices for the units digit = 4 × 4 × 4 = 64.