Use numbers 0, 1, 2, 3 and 4 to form numbers without repeating numbers. (1) how many five digit numbers can be formed? (2) how many odd five digit numbers can be formed? (3) how many positive integers can be formed?

Use numbers 0, 1, 2, 3 and 4 to form numbers without repeating numbers. (1) how many five digit numbers can be formed? (2) how many odd five digit numbers can be formed? (3) how many positive integers can be formed?


If the first digit cannot be 0, then the number of five digits is 0
4 * 4 * 3 * 2 * 1 = 96 -- number of five digits
The odd number is
2 * 3 * 3 * 2 = 36 -- odd number of five digits
4 * 4 * 3 * 2 = 96 -- four digit number
4 * 4 * 3 = 48 -- number of three digits
4 * 4 = 16 -- number of double digits
4 -- a number of positive integers
96 + 96 + 48 + 16 + 4 = 260 -- the number of positive integers without repetition



How many natural numbers can be composed of 0, 1, 2 and 3


One digit natural numbers include (0): 3 + 1
Two digit natural number: 9
Three digit natural number: 18
Four digit natural number: 18
Total: 4 + 9 + 18 + 18 = 49