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How many five digits can you make up with 12345?
There are 5 ^ 5 five digits with duplicate numbers
The number without duplicate numbers is 5 * 4 * 3 * 2 * 1 = 120
The five numbers 12345 can be used to make up the five digit number without repetition which is larger than 20000 and the white number is not 3
First of all, the number of five digits larger than 20000 composed of 12345 is calculated: because 10000 bits can only be one of 2345, so it is 4 * 4 * 3 * 2 * 1 = 96 (pieces). Then calculate the number of hundreds in which the number of hundreds is 3: because the number of hundreds has been determined to be 3, and the number of 10000 digits can only be one of 245, so it is 3 * 3 * 2 * 1 = 18 (all five digits)
How many four digits can be made up of 12345 How many four digits can be made up of 1,2,3,4,5? (the number of each digit can be repeated)
There are five possibilities for each digit: 12345
And there are four digits
According to the principle of multiplication
5*5*5*5=625
There are 625 possibilities
Using 12345 to make up the five digit number without repeating numbers, the sum of all these different five digit numbers is ()
1 + 2 + 3 + 4 + 5 = 10, same as ten, hundred, thousand and ten thousand
The sum of all these different five digit numbers is (111110 * 5 * 4 * 3 * 2 * 1 = 111110 * 120)
How many odd three digit numbers can be made up of 12345 five numbers?
There are 5, 4 out of 10 and 3 out of 100
There are three of them, four out of ten and three of hundred
There are four choices in ten and three in hundred
So there are three choices for each, four out of ten, and three out of hundred
3*4*3=36
In the three digit number of 1, 2, 3, 4, 5, the sum of each digit is the odd number in common () A. 36 B. 24 C. 18 D. 6
According to the meaning of the question, the question is a classification and counting problem,
There are two types where the sum of the numbers is odd:
① Two even numbers and one odd number: c31a33 = 18;
② All three are odd: there are A33 = 6
According to the principle of classification and counting, there are 18 + 6 = 24
Therefore, B
In the three digit number of 1, 2, 3, 4, 5, the sum of each digit is the odd number in common () A. 36 B. 24 C. 18 D. 6
According to the meaning of the question, the question is a classification and counting problem,
There are two types where the sum of the numbers is odd:
① Two even numbers and one odd number: c31a33 = 18;
② All three are odd: there are A33 = 6
According to the principle of classification and counting, there are 18 + 6 = 24
Therefore, B
There are five numbers, 12345, which make up five digits without repeating numbers, of which there are several odd numbers To find a formula for this kind of problem, All relevant formulas are required I want a formula, I mainly want the formula of this kind of problem
If it is an odd number, the end can only be 1, 3, or 5
If it ends with 1, the preceding arrangement can only be 4 × 3 × 2 × 1
End with 3.5
So there are 3 × 24 = 72
The formula is not easy to say. Suppose there are n numbers, including M odd numbers. Then there are n digits that are not repeated
m*(n-1)!
How many five digits are composed of 12345
C55 = 5 * 4 * 3 * 2 * 1 = 120
Use numbers 1, 2, 3, 4, 5 to form five digits, and find out the probability that there are exactly four same numbers
There are 55 possible results in five digits
Now find the number of results with exactly four identical numbers in five digits:
There are C51 ways to get the same number, and C41 to get another different number
And the five numbers taken out can be divided into C51 different five digits,
Therefore, the result of five digits with exactly four identical numbers is c51c41c51,
The calculated probability p = C
One
Five
C
One
Four
C
One
Five
55=4
125．
A: the probability of exactly four of the same numbers is 4
125．
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