How many four digit numbers are composed of 1, 2, 3, 4 and 5 without repetition? How many even numbers are there?

How many four digit numbers are composed of 1, 2, 3, 4 and 5 without repetition? How many even numbers are there?

There are 5 * 4 * 3 * 2 = 120 four digit numbers without repetition, which are composed of 1, 2, 3, 4 and 5
There are 120 * 2 / 5 = 48 even numbers

Use the five numbers 1, 2, 3, 4 and 5 to form a four digit number without repetition, in which the even number has______ One

According to the principle of multiplication, there are: 2 × 4 × 3 × 2, = 8 × 6 = 48; answer: there are 48 even numbers, so the answer is: 48

How many even numbers are adjacent to the number 12 If the number 0 1 2 3 4 is used to form a five digit number without repetition?
How many even numbers are adjacent to the number 12 If the number 0 1 2 3 4 is used to form a five digit number without repetition?

When the single digit is 0, arrange a (2,1) with 1,2; regard 1,2 as a whole and arrange a (3,3) with the remaining two digits
When the single digit is 2, 1 and 2 are arranged in one way; the first digit of the remaining three digits cannot be zero: C (2,1) * a (2,2)
When the single digit is 4, arrange a (2,1) with 1,2; regard 1,2 as a whole, the first digit cannot be zero: C (2,1) * a (2,2)
So the total number is: a (2,1) * a (3,3) + C (2,1) * a (2,2) + a (2,1) * C (2,1) * a (2,2)
=12 + 4 + 8 = 24
I hope I can understand it,