Current location - Training Enrollment Network - Mathematics courses - Counting principle ~ details ~ How many five-digit numbers can be formed by using the six mathematics of 0 1 2 3 4 5, which meet the following conditions and have no duplication?
Counting principle ~ details ~ How many five-digit numbers can be formed by using the six mathematics of 0 1 2 3 4 5, which meet the following conditions and have no duplication?
How many five-digit numbers can be formed by the six mathematics of 0 1 2 3 4 5, which meet the following conditions respectively and have no duplicate signs?

1.288 odd numbers

3 5 starting with 1 cannot be 0.

3 x 4 x 4x 3x 2 =288

There are 60 numbers divisible by 25.

The ending must be 00 (excluding) 25 50 75.

When ending with 25 75, 2x3x2 = 36.

4x 3x2 = 24 at the end of 50.

24+36=60

3. A number greater than 12345 and divisible by 5. 204 species

The ending must be 5 or 0.

When the ending is 5

12435 at the beginning of 1 2 can be selected as1.

135 at the beginning of13 has 3 digits in the middle, and 3x2=6 options.

145 at the beginning of14 has 3 digits in the middle, and 3x2=6 options.

There are 4 numbers in the middle 3 digits of the first 2-5, 4x3x2=24 kinds to choose from.

There are 4 numbers in the middle 3 digits of 3-5 at the beginning of 3. You can choose 4x3x2=24 kinds.

There are four numbers in the middle three digits of 4-5 at the beginning of 4. You can choose 4x3x2=24 kinds.

A * * * has 1+6x2+24x3= 85.

When ending with 0.

12350 at the beginning of 1 235 can be selected as1.

124 starts with 1 with two digits in the middle, so you can choose two.

1250 at the beginning of 1 25 has two digits in the middle of1,so you can choose two.

130 at the beginning of13 has 3 digits in the middle, and 3x2=6 options.

140 at the beginning of14 has 3 digits, and 3x2=6 options.

15 15 starts with15, and there are three numbers in the middle two digits. You can choose 3x2=6 kinds.

There are four numbers in the middle three digits of 2 0 at the beginning of 2. You can choose 4x3x2=24 kinds.

There are four numbers in the middle three digits of 3 0 at the beginning of 3. You can choose 4x3x2=24 kinds.

There are four numbers in the middle three digits of the 4 0 at the beginning of the 4. You can choose 4x3x2=24 kinds.

There are four numbers in the middle three digits of 5 0 at the beginning of 5. You can choose 4x3x2=24 kinds.

A * * * has1+2x2+6x3+24x4 =1+4+18+96 =119.

A * * *, with 1 19 +85 =204.