CAT 2001 — QA Question 47
Permutation & CombinationEasy
Let n be the number of different 5 digit numbers, divisible by 4 with the digits 1, 2, 3, 4, 5 and 6, no digit being repeated in the numbers. What is the value of n?
Answer & solution
Correct answer: 192
- A
144
- B
168
192
- D
None of these
Solution
For a number to be divisible by 4, the last two digits should be divisible by 4.
There are eight such two digit combinations that can be formed from the given digits so that no digits are repeated.
The last two digit combinations are 12, 16, 24, 32, 36, 52, 56 and 64.
∴ There are 8 ways to fill the last two places.
∴ Number of ways in which the first three places can be filled = 4 × 3 × 2 = 24
∴ Total number of ways = 24 × 8 = 192
Hence, option (c).