how many natural numbers smaller than 10^4 and divisible by 4 can be formed using 01235.

Dear Shiwani

One digit number- there will be no one digit number

two digit numbers

12,20,32,52 total 4

3 digit number

we have to fix last two digit for the divisibility by 4

last two digits can be 12,20,32,52 corresponding to these first digit can be chosen in 4 ways leaving 0 out of 5 numbers 0,1,2,3,5

so there are 4*4=16 numbers

4 digit numbers

again last two digits will be 12,20,32,52 and first digit can be chosen in 4 ways (leaving 0) and 2nd digit can be chosen in 5 ways so for each there will be 4*5=20 numbers total for all the 12,20,32,52 will be 4*20=80 numbers

there will be no 5 digit number

so total numbers will be= 4+16+80= 100 numbers

All the best.                                                           

AKASH GOYAL

AskiitiansExpert-IIT Delhi

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