Question

How many 4 digit numbers. can be formed using the digits 1,2,3,4,5 if no digit is not repeated?

• A. 24
• B. 120
• C. 80
• D. 48

Answer 1

Answer:

B. 120

120 different 4-digit numbers can be formed.

1. Identify Available Positions

A 4-digit number has four blank places to fill:
$\text{\underline{Thousands}} \quad \text{\underline{Hundreds}} \quad \text{\underline{Tens}} \quad \text{\underline{Ones}}$

2. Apply Multiplication Principle

Since digits cannot be repeated, the number of choices decreases by 1 for each subsequent position:

• Thousands place: 5 possible choices (1, 2, 3, 4, or 5)

• Hundreds place: 4 remaining choices

• Tens place: 3 remaining choices

• Ones place: 2 remaining choices

3. Calculate Total Permutations

Multiply the number of possibilities for each position together:
$\text{Total Numbers} = 5 \times 4 \times 3 \times 2 = 120$