Question

6. How many positive numbers less than 100 are possible by using the digits 0, 1, 2, 3? If the repetition of the digits is not allowed, how many such numbers are possible?
7. How many even numbers are possible between 2000 and 3000 by using the digits 0, 1, 2, 3, 4, only once? ​

Answer 1

Answer:

#6

Positive numbers less than 100 are 1 through 99.

• 1- digit = 3 numbers, zero excluded
• 2- digit = 3*4 = 12 numbers, zero excluded for the first digit

Total:

• 3 + 12 = 15 numbers

Repetition is not allowed:

• 1- digit = 3 numbers as above
• 2-digit = 3*3 = 9 numbers, minus one for the second digit

Total:

• 3 + 9 = 12 numbers

#7

abcd is the number.

• a = 2, then d = 4 or 0, b = 3 options, c = 2 options
• a = 3, no options

Total:

• 1*2*3*2 = 12 numbers