Permutation Combination Question 12
Question 12 - 30 January - Shift 1
Number of 4-digit numbers (the repetition of digits is allowed) which are made using the digits 1, 2, 3 and 5 , and are divisible by 15 , is equal to ___________
Show Answer
Answer: 21
Solution:
Formula: Permutation with repitition, Divisibility of numbers
Sol. For number to be divisible by 15 , last digit should be 5 and sum of digits must be divisible by 3 .
Possible combinations are
| 1 | 2 | 1 | 5 |
|---|
Numbers $=3$
| 2 | 2 | 3 | 5 |
|---|
Numbers $=3$
| 3 | 3 | 1 | 5 |
|---|
Numbers $=3$
| 1 | 1 | 5 | 5 |
|---|
Numbers $=3$
| 2 | 3 | 5 | 5 |
|---|
Numbers $=6$
| 3 | 5 | 5 | 5 |
|---|
Numbers $=3$
Total Numbers $=21$
