First question
First of all, the solution upstairs (4th and 5th floors) is correct. You can also think of it this way: when two sons are at the same level, one * * has10 * p (9,2) =10 * 9 * 8 = 720 possibilities. Here, P is the permutation symbol (C, followed by the combination symbol), 9 is the subscript, 2 is the superscript, and P is used instead of C because the red car and the black car are two different individuals. When two sons are on the same vertical line, * * has 9 * p (10/0,2) = 9 *10 * 9 = 810, so the total answer is 1530.
the second question
To be an even number, the last digit must be 2, 4, 6 or 8, and the remaining eight digits must be arranged arbitrarily. Even * * * has C (4,1) * p (8,8) =161280.
Because they are randomly arranged, the number divisible by 4 must be half of an even number. The following proofs:
If a number is divisible by 4, then the last two digits need to be divisible by 4. It is easy to get a detailed list, 12, 32, 52, 72, 92, 24, 64, 84, 16, 36, 56, 76, 96, 28, 48, 68 * * 68. The result is c (16,1) * p (7,7) = 80640 verifications, which is just half of the even number.
Third question
Because B is in the middle, B is not considered, and four letters are put in the remaining four positions.
Because A is not in the first place, there are three arrangements of A.. The remaining three letters are randomly arranged. The result is C(3,1) * p (3,3) =18 species.
The fourth question
There is only one restriction, that is, two boys are at both ends, so choose two boys to stand at both ends, and the remaining nine people will be arranged at will. P (8,2 2) * P (9 9,9) = 20321280 It is difficult to calculate without a calculator. .
The idea upstairs is right, and the result is the same.
The fifth question
The three majors that are restricted to male students are P (10/0,3) = 720.
There are * * * P (5 5,2) = 20 ways to recruit girls.
After the recruitment, there are two gender-neutral recruitment methods: p P( 10/0,2) = 720. The result is 720*20*720= 1036800 kinds of picking methods. The result of this question upstairs is wrong, so P should be used instead of C, because every boy and girl is an independent individual.
I hope I can help you.