Question

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

Answer 1

Number of 6 digit number that can be formed without 1 is 3*3*3*3*3*3 = 729

This is because each place now can be filled with only 3 remaining numbers

Similarly the number of 6 digit numbers that can be formed without 2,3,4 are 729 respectively.

Totally the number of numbers without one of the digits is 729 * 4 = 2916

The total number of 6 digit numbers that can be formed = 4*4*4*4*4*4 = 4096

So the answer is 4096 - 2916 = 1180

Answer 2

Answer:

Step-by-step explanation:

Out of the six digits,  four digits are fixed.

In the remaining two digits, both the digits could be same  or both the digits could be different as well

Case one - When both the digits are same.

Number of six digit numbers =4C1 × 6! /3!

(Both the digits could be any of the four digits, therefore 4C1)

Case two - When both the digits are different.

(The two digits could be any two of the four digits, therefore 4C2)

Therefore,  the number of six digit numbers in this case = 4C2 × 6!/2!.2!

Thus, the required number of 6 digit numbers = 4C1 × 6!/3! + 4C2 × 6!/2!.2! +

= 6! (23+32)

= 6! × 136

= 1560

Thus, the required number is 1560.