00:01
Hey, it's clarissa when you read here.
00:02
So all positive integers, less than 1 million, have at most 6 digits.
00:08
So we're going to let x sub i be the ith digit of a positive integer less than 1 million.
00:14
And i is going to be between 1 through 6 included.
00:30
So we have the equation x sub 1 plus x sub 2 plus x sub 3.
00:40
Plus x sub 4 plus x sub 5 plus x sub 6 has to be equal to 19.
00:56
And x sub i are digits 0 through 9 included and i is from 1 through 9.
01:03
So we know that repetition is allowed since more than 1 x sub i value can take on the same value.
01:10
And its combination since the order of the solutions is not important.
01:14
So that gives us the formula c of n plus r minus 1 comma r is equal to n plus r minus 1 factorial all over r factorial times and minus 1 factorial.
01:37
So we're first going to look at the number of solutions with no restrictions on x sub i's.
01:47
So we want to select 19 indistinguishable objects from six distinguishable boxes...