Question

Number of $4$ digit numbers that can be formed using digits $0,1,2,3,4,5$ which are divisible 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 the 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 be there and thousands place can be filled in $3$ ways.

Case $2:$ When last three digit does not contain $0$.
Total $5$ cases will be there and thousands place can be filled in $2$ ways.

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