CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
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, 9

Case 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=64

Case 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=72

Case 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=9

Case 5:
Single digit number that ends with 5 is 1.
From all five cases,

Total number of ways =64+72+8+9+1=154

Hence, Option A is correct.


flag
Suggest Corrections
thumbs-up
6
BNAT
mid-banner-image