Number of natural numbers smaller than 10000 and divisible by 4 which can be formed using the digits 0, 1, 2, 3 & 5 if repetition of digits is not allowed is..................................
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Sol. Two digit number divisible by 4
12, 20, 32, 52
Three digit number divisible by 4
if last two digit is 12, 32 or 52 remaining can be filled in two ways
2 × 3 = 6 ways
if last two is 20 first can be filled in 3 ways
Total 3 digit number divisible by 4 = 6 + 3 = 9
Total four digit number divisible by 4
if last two are 12, 32, 52 remaining can be filled in 2 × 2 × 3 ways.
if last two are 20 remaining can be filled in 2 × 3 ways
Total numbers are = 4 + 9 + 12 + 6 = 31
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