wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A five digit number divisible by 3 has to be formed using the numerals 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is


A

216

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

240

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

600

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

3125

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A

216


We know that a five digit number is divisible by 3, if and only if sum of its digits (= 15) is divisible by 3, therefore we should not use 0 or 3 while forming the five digit numbers.

Now,

(i) In case we do not use 0 the five digit number can be formed (from the digit 1, 2, 3, 4, 5) in 5P5 ways.

(ii) In case we do not use 3, the five digit number can be formed (from the digit 0, 1, 2, 4, 5) in 5P54P4 = 5! - 4!= 120 - 24 = 96 ways.
(4P4= cases when 0 is at the first position)

The total number of such 5 digit number = 5P5+(5P54P4)=120+96=216


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon