    Question

# A 5 digit number is formed by using the digits 0,1,2,3,4 and 5 without repetition. The probability that the number is divisible by 6 is:

A
8%
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
17%
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
18%
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
36%
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is C 18%Total 55 digit numbers formed by the given digits=5∗5!=6005∗5!=600For divisibility by 6, the numbers must be divisible by both 2 and 3.Only numbers formed by digits (i) (0,1,2,4,5) and (ii) (1,2,3,4,5) are divisible by 3.(i) CASE 1: ( 0,1,2,4,5) For divisibility by 2, _ _ _ _ _(a) if 0 is placed at the end, then number of ways=4!=24 (b) if 0 is not placed in the end, then there are two ways to select the last digit(2,4). Number of ways=2*3*3!=362C1∗3C1∗3!=36 For this case, total number of ways=24+36=60(ii) CASE 2: ( 1,2,3,4,5) Again, the last number can be chosen in 22C1 ways and the remaining 4 numbers can permute in 4!4! ways. The required number of ways for this case= 2∗4!=482∗4!=48Adding the number of ways in the two cases, 5 digit numbers that are divisible by 6= 108Required Probability = 108600=108600=0.18==18%  Suggest Corrections  0      Similar questions
Join BYJU'S Learning Program
Select...  Related Videos   Defining Probability
MATHEMATICS
Watch in App  Explore more
Join BYJU'S Learning Program
Select...