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Quantitative Aptitude Question on Permutation and Combination

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

A

2442

B

2222

C

3333

D

2592

Answer

2222

Explanation

Solution

To find the arithmetic mean of all the distinct numbers that can be obtained by rearranging the digits in 1421,we first need to determine all the possible permutations of the digits.Then,we'll calculate the sum of these permutations and divide by the total number of permutations to find the mean.
The number 1421 has 4 distinct digits:1,2,4, and 2(repeated).
Total number of permutations=4!2!\frac{4!}{2!}(since '2' is repeated)=12
Now, let's list all the distinct permutations:
1241
1214
1421
1412
2141
2114
2411
2411
4121
4112
4211
4211
Now,calculate the sum of these permutations:
Sum=1241+1214+1421+1412+2141+2114+2411+2411+4121+4112+4211+4211=27170
Finally,calculate the mean:

Mean=SumTotal  number  of  permutations\frac{Sum}{Total\space number\space of\space permutations}

= 2717012\frac{27170}{12}≈ 2264.167
The closest option to this mean is option (B).

So,the correct answer is (B): 2222