Find the sum of all 4 digit numbers made from digits 1,2,3,4 (repetitions not allowed)
Answers
No. of 4 digits numbers made using digits 1, 2, 3, 4 without repetition = 4! = 24.
Among these 24 numbers, there are 3! = 6 numbers each in which each digit 1, 2, 3 and 4 are repeated at each places, ones place, tens place, hundreds place and thousands place.
⇒⇒ Sum of place values of each digit 1, 2, 3, 4 which repeated 6 times at thousands place = 6(1000 + 2000 + 3000 + 4000) = 6 × 10000 = 60000.
⇒⇒ Sum of place values of each digit 1, 2, 3, 4 which repeated 6 times at hundreds place = 6(100 + 200 + 300 + 400) = 6 × 1000 = 6000.
⇒⇒ Sum of place values of each digit 1, 2, 3, 4 which repeated 6 times at tens place = 6(10 + 20 + 30 + 40) = 6 × 100 = 600.
⇒⇒ Sum of place values of each digit 1, 2, 3, 4 which repeated 6 times at ones place = 6(1 + 2 + 3 + 4) = 6 × 10 = 60.
→ → → Thus, the total sum of the all 24 numbers
= 60000 + 6000 + 600 + 60
= 66660