Question

# A four digit number is formed using the digits 0, 1, 2, 3, 4 without repetition. Find the probability that it is divisible by 4.

A

3/4

No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
B

1/4

No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
C

5/16

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

7/20

No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
Open in App
Solution

## The correct option is C 5/16 We will first find the total number of four digits numbers which can be formed using 0, 1, 2, 3 and 4, without repetition. Let the number be like a–– b– c– d––. 'a' can be any of the numbers 1, 2, 3 and or 4. It can't be zero, because then it will become a 3 digit number. Second digit can be filled in 4 ways. [One of the digits of 0, 1, 2, 3 and 4 got used as 'a'. There will be four digits left]. Similarly, c and d can be filled in 3 and 2 ways. ⇒ total number of numbers =4×4×3×2 Now we want to find the total number of favorable outcomes. That is, the numbers which are divisible by 4. There can be numbers of the form a––b– 12,a––b–24,a––b–32, which did not use zero yet and numbers which are of the form a––b–04,a––b–20 and a––b–40 which has used zero. In numbers of the form a b 12, we can fill 'a' in 2 ways, and 'b' in 2 ways. So there will be 3×(2×2) numbers of that form. Similarly, for numbers of the form a b 04, there can be 3×(3×2) ways of filling a and b. ⇒ Total number of favorable outcomes =Total number of 4-digit numbers divisible by 4 =3×(3×2)+3×(2×2) =3 × 10 = 30 ⇒ Probability =304×4×3×2 =516

Suggest Corrections
2
Join BYJU'S Learning Program
Select...
Related Videos
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
Select...