Question

Consider the digits 3, 5, 7, 9. What is the number of 5-digit numbers formed by these digits in which each of these four digits appears?
1. 240
2. 180
3. 120
4. 60

Answer 1

Correct Answer - Option 1 : 240

Formula used:

n! = n × (n - 1) × (n - 2) × ..... × 3 × 2 × 1

5! = 5 × 4 × 3 × 2 × 1 = 120

2! = 2 × 1 = 2

Calculation:

Four cases: (3, 5, 7, 9, 3)......(3, 5, 7, 9)

For (3, 5, 7, 9, 3)

= \(\rm \frac{5!}{2!}\)

= \(\rm \frac{120}{2}\)

= 60

Similarly for all 4 cases 60 ways 

= 60 × 4

= 240