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Question

Find the sum of all 4digit numbers that can be formed using the digits 0,2,4,7,8 without repetition.

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Solution

Solution:
The number of 4digit numbers formed by using 0,2,4,7,8 without repetition =5P44P3=12024=96.
Out of these 96 numbers,
4P33P2 numbers contain 2 in units place.
4P33P2 numbers contain 2 in tens place.
4P33P2 numbers contain 2 in hundreds place.
4P3 numbers contain 2 in units place.
The values obtained by adding 2 in all numbers.
=(4P33P2)2+(4P33P2)20+(4P33P2)200+4P2×2000
=4P3(2+20+200+2000)3P2(2+20+200)
=24×22226×222
=24×2×11116×2×111
Similarly, the value obtained by adding 4 is 24×4×11116×4×111.
The value obtained by adding 7 is 24×7×11116×7×111.
The value obtained by adding 8 is 24×8×11116×8×111.
The sum of all numbers
=(24×2×11116×2×111)+ (24×4×11116×4×111)+ (24×7×11116×7×111)+ (24×8×11116×8×111)
=24×1111×(2+4+7+8)6×111×(2+4+7+8)
=26664×21666×21
=55994413986
=545958

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