Question

Number of $4$ digit numbers using digits $0,1,2,3,4,5$ which are divisble by $8$, when each digit is used at most once is

• A. $32$
• B. $37$
• C. $33$
• D. $31$

Answer 1

The correct option is B $37$

Any number is divisible by 8 if last three digit is divisible by $8$

$024,032,104,120,152,240,304,312,320,352,432,504,512,520$
Case $1:$ when last three digit contains $0$,
total $9$ cases will there and thousands place can be filled in $3$ ways
Case $2:$ when last three digit does not contains $0$,
total $5$ cases will there and thousands place can be filled in $2$ ways

Total required numbers$=9\times 3+5\times 2=37$