The arithmetic mean of all the distinct numbers that can be obtained by rearranging the digits in 1421, including itself, is
Explanation:
8. Let us consider the sum of unit’s digit of all such numbers. __ __ __ x If 1 occupies the units digit, number of such numbers = 3! = 6 Sum of all the units digit of such numbers = 6 × 1 = 6
If 2 occupies the units digit, number of such numbers = 3!/2! = 3 Sum of all the units digit of such numbers = 3 × 2 = 6
If 4 occupies the units digit, number of such numbers = 3!/2! = 3 Sum of all the units digit of such numbers = 3 × 4 = 12
∴ Sum of unit’s digits of all possible numbers = 6 + 6 + 12 = 24
Similarly, Sum of ten’s digits of all possible numbers = 24 × 10 = 240 Sum of hundred’s digits of all possible numbers = 24 × 100 = 2400 Sum of thousand’s digits of all possible numbers = 24 × 1000 = 24000
⇒ Sum of all such numbers = 24 + 240 + 2400 + 24000 = 26664 Also, number of such numbers = 4!/2! = 12
∴ Average of all such numbers = 2664/12 = 2222
Hence, option (a).
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