The total number of four digit numbers such that each of first three digits is divisible by the last digit, is equal to ____________.
Answer (integer)
1086
Solution
If unit digit is 1 then $\rightarrow 9 \times$ s $10 \times 10=900$ numbers <br/><br/>If unit digit is 2 then $\rightarrow 4 \times 5 \times 5=100$ numbers <br/><br/>If unit digit is 3 then $\rightarrow 3 \times 4 \times 4=48$ numbers<br/><br/> If unit digit is 4 then $\rightarrow 2 \times 3 \times 3=18$ numbers<br/><br/> If unit digit is 5 then $\rightarrow 1 \times 2 \times 2=4$ numbers <br/><br/>If unit digit is 6 then $\rightarrow 1 \times 2 \times 2=4$ numbers
<br/><br/>
For $7,8,9 \rightarrow 4+4+4=12$ Numbers
<br/><br/>
Total $=1086$ Numbers
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle
This question is part of PrepWiser's free JEE Main question bank. 135 more solved questions on Permutations and Combinations are available — start with the harder ones if your accuracy is >70%.