The sum of all the four-digit numbers that can be formed using all the digits 2, 1, 2, 3 is equal to __________.
Answer (integer)
26664
Solution
We have, four digits are $2,1,2,3$.
<br/><br/>Total numbers when 1 is at unit digit $=\frac{3 !}{2 !}=3$
<br/><br/>Total number when 2 is at unit digit $=3 !=6$
<br/><br/>Total numbers when 3 is at unit digit $=\frac{3 !}{2 !}=3$
<br/><br/>Sum of digits at unit place $=3 \times 1+6 \times 2+3 \times 3=24$
<br/><br/>$\therefore$ Required sum $=24 \times 1000+24 \times 100+24 \times 10+24 \times 1$
<br/><br/>$=24 \times 1111=26664$
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle
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