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

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Filo · Accepted Answer

Solution:The number of 4−digit numbers formed by using 0,2,4,7,8 without repetition =5P4​−4P3​=120−24=96.Out of these 96 numbers,4P3​−3P2​ numbers contain 2 in units place.4P3​−3P2​ numbers contain 2 in tens place.4P3​−3P2​ numbers contain 2 in hundreds place.4P3​ numbers contain 2 in units place.∴ The values obtained by adding 2 in all numbers.=(4P3​−3P2​)2+(4P3​−3P2​)20+(4P3​−3P2​)200+4P2​×2000=4P3​(2+20+200+2000)−3P2​(2+20+200)=24×2222−6×222=24×2×1111−6×2×111Similarly, the value obtained by adding 4 is 24×4×1111−6×4×111.The value obtained by adding 7 is 24×7×1111−6×7×111.The value obtained by adding 8 is 24×8×1111−6×8×111.∴ The sum of all numbers=(24×2×1111−6×2×111)+ (24×4×1111−6×4×111)+ (24×7×1111−6×7×111)+ (24×8×1111−6×8×111)=24×1111×(2+4+7+8)−6×111×(2+4+7+8)=26664×21−666×21=559944−13986=545958

Question Text	Find the sum of all $4 - d i g i t$ numbers that can be formed using the digits $0, 2, 4, 7, 8$ without repetition.
Answer Type	Text solution:1
Upvotes	150

Find the sum of all $4 - d i g i t$ numbers that can be formed using the digits $0, 2, 4, 7, 8$ without repetition.

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