Permutation and Combination - Quant/Math - CAT 2013
Question 4 the day:
August 30, 2002
The question for the day is from the topic of permutation and combination.
- How many five digit numbers can be formed using the digits 0, 1, 2, 3, 4 and 5 which are divisible by 3, without repeating the digits?
| (1) |
15 |
|
(2) |
96 |
|
(3) |
216 |
|
(4) |
120 |
Correct Answer - (3)
Solution:
There are six digits - 0, 1, 2, 3, 4 and 5. To form 5-digit numbers we need exactly 5 digits. So we should not be using one of the digits.
The sum of the numerals 0, 1, 2, 3, 4 and 5 is 15. We know that a 5-digit number is divisible by 3 if an only if the sum of its digits are divisible by '3'. Therefore, we should not use either '0' or '3' while forming the five digit numbers - only then will it be divisible by '3'.
If we do not use '0', then the remaining 5 digits can be arranged in 5! ways = 120 numbers.
If we do not use '3', then the remaining arrangements that are possible without '0' being the first digit are 5! - 4! = 120 - 24 = 96 numbers.
Therefore, there are a total of 120 + 96 such numbers that exist.
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