Question

What is the sum of all 4 digits numbers that can be formed using all digits 2,3,5,7?

Answer 1

There are four digits = 2 , 3 , 5 , 7

How many numbers could be formed by these four numbers ?

4⁴ / 4 = 64 combinations

Now, the part to understand is these 4 numbers would repeat in ones,tens, hundreds and thousands place,

The sum would be

64 × ( 2 + 3 + 5 + 7 ) + 64 × 10 × ( 2 + 3 + 5 + 7 ) + 64 × 100 ( 2 + 3 + 5 + 7 ) + 64 × 1000 × ( 2 + 3 + 5 + 7 )

= 64 × 17 × ( 1 + 10 + 100 + 1000 )

= 64 × 17 × 1111

= 1208768 is the required answer

Answer 2

Heya Mate

^_^ Basic Multiplication Principle ✓✓

✓✓ Here it goes :

(•) Fix a number on the 1000'th place, say 2

Clearly, hopefully we can make 4³ numbers out of the rest places

(•) Note that the numbers being all distinct denies any possibility of repetition. And so, you can without a doubt claim that :

The sum would be :

${4}^{3} (2 + 3 + 5 + 7)( {10}^{3} + {10}^{2} + 10 + 1)$
How ?

=_= Since every four digit number such as 2357 can be written as 2000 + 300 + 50 + 7 Can it not ?

And there you go with your sum +_+

The Ans -> 1208768

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Hope you find your answer