There are six numbers from 0 to 5. 1. How many numbers can be made up without repetition? ② How many even digits can be made up of 5 digits without repetition? ③ How many digits are larger than 24305 among the five digits that can be composed of no duplicate digits?

There are six numbers from 0 to 5. 1. How many numbers can be made up without repetition? ② How many even digits can be made up of 5 digits without repetition? ③ How many digits are larger than 24305 among the five digits that can be composed of no duplicate digits?

Solution & nbsp; & nbsp; (1) The six numbers from 0 to 5 can be composed of 1-digit A61 = 6, 2-digit A51 × A51 = 25, 3-digit A51 × a52 = 100, 4-digit A51 × A53 = 300, 5-digit A51 × a54 = 600, 6-digit A51 × A55 = 600, so a total of 6 + 25 + 100 + 300 + 600 + 600 = 1631 can be formed; (2) according to the meaning of the title, it is required to be 5-digit and the first one cannot be changed If it is 0, then the digit must be even. The discussion can be divided into three situations: ① if there is no 0 in the 5 digits, there are A21 methods for the individual digit, and the rest have A41 methods, then there are a total of a21a41 = 48; ② if there is 0 in the 5 digits and 0 is in the individual digit, there are a total of a54 = 120; ③ if there is 0 in the 5 digits and 0 is not in the individual digit, there are a31a21a43 = 144; there are 48 + 120 + 144 = 312. (3) according to the meaning of the question, the discussion can be divided into four situations: ① the first place is 3, 4 The five digits of 5 meet the requirements, a 31a 54 = 360, followed by a 43 = 24 for the first two digits of 25, a 32 = 6 for the first three digits of 245, and 4 for the first three digits of 243, which are larger than 24305. A total of 360 + 24 + 6 + 4 = 394