unusual sum

Probability Level 2

find the sum of all 5 digit formed using the numbers - 2,4,5,6,8 without repetition


The answer is 6666600.

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Utkarsh Grover by Utkarsh Grover , 22, India

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1 solution

Utkarsh Grover
Oct 22, 2014

sum due to unit digits ; 4! * (2+4+5+6+8) = 600 ; sum of digits at tens place ; 4! * (2+4+5+6+8) *10 = 6000 ; similarly sum of digit at hundreds place =60000 ; thousands =600000 ; ten thousands = 6000000 ; adding them all ,we get 6666600

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Whatever the number the sum of their digits is (2+4+5+6+8) =25. Any digit can be at 10000, 1000, 100, 10, or 1 place. this gives us 11111 options. Once a digit is placed in any of the five position given above, 4 places to be filled with 4 digits, they have 4! =24 options.............................
Thus we have 25 * 11111 * 24 = 6666600 options.

Niranjan Khanderia - 6 years, 7 months ago

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