1. Tardigrade
  2. Question
  3. Mathematics
  4. A list is made of all the 3 digit numbers whose digits are 1, 2, 3, 4 or 5 with no repetition. If the sum of all the numbers is 10 N, then find the value of N.

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. A list is made of all the 3 digit numbers whose digits are 1, 2, 3, 4 or 5 with no repetition. If the sum of all the numbers is 10 N, then find the value of N.

Permutations and Combinations

Solution:

Total 3 digit numbers $={ }^5 C _3 \times 3 !=60$
Sum of each column $=12[1+2+3+4+5]=180$
Hence sum $=1998 \times 10 \Rightarrow N =1998$
image
Alternative : Digit 1, 2, 3, 4, 5 are in A.P. and
hence sum of all the 3 digit numbers is $\frac{3 !}{2}(123+543)=3 \times 666=1998$