SOLUTION: How many three digit numbers can be formed from the set 0-9 if repetition are allowed and the number must be a) even b) divisible by 5? c)divisible by 10?

Choose the first digit as any of these 9 ways: {1,2,3,4,5,6,7,8,9}
Choose the second digit as any of these 10 ways: {0,1,2,3,4,5,6,7,8,9}
Choose the third digit as any of these 5 ways: {0,2,4,6,8}

Answer: 9×10×5 = 450 ways.

Choose the first digit as any of these 9 ways: {1,2,3,4,5,6,7,8,9}
Choose the second digit as any of these 10 ways: {0,1,2,3,4,5,6,7,8,9}
Choose the third digit as either of these 2 ways: {0,5}

Answer: 9×10×2 = 180 ways.

Choose the first digit as any of these 9 ways: {1,2,3,4,5,6,7,8,9}
Choose the second digit as any of these 10 ways: {0,1,2,3,4,5,6,7,8,9}
Choose the third digit as this 1 way: {0}

Answer: 9×10×1 = 90 ways.

Edwin