CAT 2022 Slot 3 QA Question 15: The arithmetic mean of all the distinct numbers that can be obtained by rearranging the digits in 1421, including itself, is

Question

The arithmetic mean of all the distinct numbers that can be obtained by rearranging the digits in 1421, including itself, is

Accepted Answer

The digits are 1, 1, 2 and 4.
Number of distinct arrangements = $\dfrac{4!}{2!} = 12$
Across all 12 numbers, in any one place, the digit 1 appears 6 times, the digit 2 appears 3 times and the digit 4 appears 3 times.
Sum of digits in one place = $6 	imes 1 + 3 	imes 2 + 3 	imes 4 = 24$
This same