if repeated digits are not allowed the number of four digit even numbers that can be formed from the digits 0,1,5,6,7,8,9 is
To find the number of four-digit even numbers that can be formed using the digits 0, 1, 5, 6, 7, 8, and 9 without any repeated digits, we need to consider a few conditions:
1. The last digit must be even. Thus, it can only be 0, 6, or 8.
2. The first digit cannot be 0 because a four-digit number cannot start with a leading zero.
Now, let's break down the problem into different cases based on the last digit:
Case 1: The last digit is 0.
In this case, the last digit is fixed, and we need to choose the first digit from the remaining available digits. We have 6 choices for the first digit (1, 5, 6, 7, 8, or 9). Once the first digit is chosen, there are 5 remaining digits, and for the second digit, we have 5 choices. For the third digit, we have 4 choices, and for the fourth digit, we have 3 choices.
So, the number of four-digit even numbers ending with 0 is: 6 * 5 * 4 * 3 = 360.
Case 2: The last digit is 6.
Using a similar logic as in Case 1, we have 6 choices for the first digit (1, 5, 7, 8, or 9). After choosing the first digit, there are 5 remaining digits, and for the second digit, we have 4 choices. For the third digit, we have 3 choices, and for the fourth digit, we have 2 choices.
So, the number of four-digit even numbers ending with 6 is: 6 * 5 * 4 * 2 = 240.
Case 3: The last digit is 8.
Again, using a similar logic as in Case 1, we have 6 choices for the first digit (1, 5, 6, 7, or 9). After choosing the first digit, there are 5 remaining digits, and for the second digit, we have 4 choices. For the third digit, we have 3 choices, and for the fourth digit, we have 2 choices.
So, the number of four-digit even numbers ending with 8 is: 5 * 5 * 4 * 2 = 200.
Therefore, the total number of four-digit even numbers that can be formed without repeated digits using the digits 0, 1, 5, 6, 7, 8, and 9 is: 360 + 240 + 200 = 800.
6{08}x{80}: 2*5 = 10
6x{08}{80}: 5*2 = 10
same for leading 8: 20
{1579}<odd><odd>{068}: 4*3*2*3 = 72
{1579}<odd><even>{068}: 4*3*3*2 = 72
same for {1579}<even><odd>{068}: 72
Looks like 256 in all
Double-check to see whether I missed something.