The total number of natural numbers of 6 digits that can be made with digits 1,2,3,4 , if all digits are to appear in the same number at least once, is

Step-by-step solution

There can be 2 types of numbers. (i) Any one of the digits 1, 2, 3, 4 repeats thrice and the remaining digits only once i.e., of the type 1,2 , 3,4,4,4 . (ii) Any two of the digits 1, 2, 3, 4 repeat twice and the remaining two only once i.e., of the type 1,2,3 , 3,4,4 . Number of numbers of the type 123444 = 6! 3! ^4 C₁=480 Number of numbers of the type 123344 = 6! 2!2! ^4 C₂=1080 So, the required number =480+1080=1560