1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# The number of natural numbers less than 1000 that are divisible by 5 in which no digit occurs more than once in the same number is

A
154
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
136
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
144
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
152
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## Digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9Case 1:Number of 3 digit numbers that end with 5(–,–,5)For first blank =8P1=8 [Since, 0 can’t be first place]For second blank =8P1=8 [Since, out of 10 numbers two numbers already filled]Number of 3 digit numbers that end with 5=8×8=64Case 2:Number of 3 digit numbers that end with 0(–,–,0)For first blank =9P1=9 For second blank =8P1=8 [Since, out of 10 numbers two numbers already filled]Number of 3 digit numbers that end with 0=9×8=72Case 3: Number of 2 digit numbers that end with 5(–,5)In blank =8P1=8 [Since, 0 can’t be first place]Case 4: Number of 2 digit numbers that end with 0(–,0)In blank =9P1=9Case 5: Single digit number that ends with 5 is 1.From all five cases,Total number of ways =64+72+8+9+1=154Hence, Option A is correct.

Suggest Corrections
25
Join BYJU'S Learning Program
Related Videos
MATHEMATICS
Watch in App
Join BYJU'S Learning Program