00:01
Hello! so the first part of this question says, how many seven -digit numbers have no repeated digits? okay, well we can count the possibilities for each digit in the number.
00:09
So the first digit cannot be zero, so we have nine choices, right? one through nine.
00:15
The second choice can be any of the remaining nine digits.
00:18
Again, zero and the first choice are excluded.
00:22
And then the third digit can be, we can choose from the remaining eight digits, and then seven choices, then six choices, then five choices, then four choices.
00:29
So we have nine, and then we have another nine, so nine times nine, and then we have times eight, seven, six, five, times four, which is going to be equal to 326 ,592.
00:48
So therefore, there are 326 ,592 seven -digit numbers with no repeated digit...