If 1 = 5,2 = 12,3 = 123,4 = 1234, then 5 =?

If 1 = 5,2 = 12,3 = 123,4 = 1234, then 5 =?


1 = 5, of course 5 = 1



How many kinds of 4-digit 2-digit continuous 2 are there with 123?


If all four numbers are two, there is one,
If 4 numbers have 3 2, there are 8 kinds of C21 * 4
If there are 2 2 of 4 numbers, there are 3 + 3 + A33 = 3 + 3 + 6 = 12,
So there are: 1 + 8 + 12 = 21 species



From the numbers 1, 2, 3 Among the three digit numbers composed of 9, the number of each digit in strict increasing (e.g. "156") or decreasing (e.g. "421") order is ()
A. 120B. 168C. 204D. 216


According to the meaning of the question, this question is a step-by-step counting problem. First of all, three numbers should be selected from nine numbers. When the three numbers are determined, the three numbers are arranged in strict ascending or descending order. There are two situations. According to the step-by-step counting principle, there are 2c93 = 168, so B is selected



How many (1) four digits can be made up of numbers 0, 1, 2, 3 and 4? (2) Four even numbers? (3) Four digits without repeating numbers? (4) Four even numbers without repeating numbers?


(1) ∵ the highest order of this four digit number can not be 0, so there are four ways to choose the highest order (i.e. choose any number from 1 to 4), and the rest of you can choose from the five numbers from 0 to 4, so there are a total of 4 × 5 × 5 × 5 = 500 four digit numbers; (2) the even number can also be obtained by a similar method, with 4 × 5 × 5 × 3 = 300; (3) ∵ the highest order of this four digit number can not be 0, so there is the highest order There are four choices (i.e. choosing any number from 1 to 4), four choices for the third digit, three choices for the second digit, and two choices for the first digit. According to the principle of multiplication, there are 4 × 4 × 3 × 2 = 96 four digits without repeated digits; (4) when the four digits are odd, there are two choices for one digit and three choices for three digits. Because the number is not repeated and the thousand digit cannot be zero, there are three choices for thousand digits, There are three ways to choose the hundred digits and two ways to choose the ten digits, so the odd number is 2 × 3 × 3 × 2 = 36, and the even number is 96-36 = 60