find the number of 6 digit numbers that can be made with digits 1,2,3,4 if all digits are to appear in the number atleast once
Hello, prasum!
Find the number of 6-digit numbers that can be made with digits {1, 2, 3, 4}
if all digits are to appear in the number at least once.
Let the four digits be:
Select one of each digit: .
There are two cases to consider.
[1] The other two digits are the same: . choices.
. . .The number is of the form:
. . .The digits can be permuted in: ways.
. . .Hence, there are: . such numbers.
[2] The other two digits are different: . choices.
. . .The number is of the form:
. . .The digits can be permuted in ways.
. . .Hence, there are: . such numbers.
The answer is: . numbers.