The numbers 2, 3, 4 and 5 can form 256
different four digit numbers. If the digits
repeat, two of the numbers are 2222 and
2223. Find the sum of all the 256 numbers.
Answers
Answer:
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Answer:
995456
Step-by-step explanation:
Number of digits = 4 {2,3,4,5}
Total no of possible arrangements(with repetition) = 4 x 4 x 4 x 4 = 256
Consider {2, 3, 4, 5} as 1 set.
Total number of sets = No of possible arrangements / No. of digits
= 256 / 4 = 64
Value of one set = 2 + 3 + 4 + 5 = 14
Value of 64 sets = 64 x 14 = 896
At ones place, the sum of all the digits = 896 x 1 = 896
At tens place, the sum of all the digits = 896 x 10 = 8960
At hundreds place, the sum of all the digits = 896 x 100 = 89600
At thousands place, the sum of all the digits = 896 x 1000 = 896000
Total sum = 896 + 8960 + 89600 + 896000 = 995456