Find the sum of all the four digit numbers that can be formed using the digits…
2023
Find the sum of all the four digit numbers that can be formed using the digits 2,3,5,9. No digit is to be repeated.
Answer: B. 126654 — Key idea: Each digit appears equally often in each place value. There are 4 digits (2, 3, 5, 9). Fixing any one place, the other 3 digits can be arranged in…
- A.
133698
- B.
126654
- C.
147896
- D.
123759
Attempted by 16 students.
Show answer & explanation
Correct answer: B
Key idea: Each digit appears equally often in each place value.
There are 4 digits (2, 3, 5, 9). Fixing any one place, the other 3 digits can be arranged in 3! = 6 ways, so each digit appears 6 times in each place.
Sum of the digits = 2 + 3 + 5 + 9 = 19.
Contribution of all digits to a single place = 19 × 3! = 19 × 6 = 114.
Total sum over all place values = 114 × (1000 + 100 + 10 + 1) = 114 × 1111 = 126654.
Answer: 126654