CAT 2022 Permutations and Combinations Question (Medium)

Question

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

Accepted Answer

2222 Why 1. The multiset of digits is 1,1,2,4 . In all distinct 4-digit rearrangements, by symmetry each place thousands, hundreds, tens, units has the same expected digit the average of the multiset. 2. Average digit . 3. Therefore the mean number .

CAT 2022

Quantitative

Permutations and Combinations

Medium

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

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