India's Largest Education Online Store: StudyNeeds.com | For questions call: 011-456-293-45 | Log In Here | Create Free Account
-
3. A five digit number is formed by using the digits 1, 2, 3,
4 and 5 without repetitions. What is the probability
that the number is divisible by 4?
(1) 1/5 (2) 5/6
(3) 4/5 (4) None of these
Answers (1)
-
The condition for any number to be divisible by 4 is that the last two digits taken together must be a multiple of 4
The digits given are - 1,2,3,4,.5
Now the last two digits must be a multiple of 4
There are 4 cases : 12 , 24 , 32 , 52 . So if the last two digits are these numbers then the five digit number formed would be divisible by 4
(a) If the last two digits are 12 , then the remaining 3 places can be filled in 3! ways
(b) if the last two digits are 24 , then the remaining 3 places can be filled in 3! ways
(c) if the last two digits are 32 , then the remaining 3 places can be filled in 3! ways
(d) if the last two digits are 52 , then the remaining 3 places can be filled in 3! ways
Total numbers which are divisible by 4 = 4 .3!
Total number of 5 digit numbers = 5!
Probability = (4.3!)/5! = 1/5