If numbers from 1 to 7 can form a 7-digit number that is not divisible by 5, then what is the 2000th number in small to large order?
Answers
Answer:
All the 7-digit numbers containing each of the digits 1, 2, 3, 4, 5, 6, 7 exactly once, and not divisible by 5, are arranged in the increasing order. ...
Answer:
here it is
Step-by-step explanation:
Ans:
Total No. of 7 digits containing each of the digits 1, 2, 3, 4, 5, 6, 7 exactly once, and not divisible by 5 = 6X6X5X4X3X2X1 = 4320
Starting with 1, total No. of 7 digits containing each of the digits 1, 2, 3, 4, 5, 6, 7 exactly once, and not divisible by 5 = 1X5X5X4X3X2X1 = 600
Starting with 2, total No. of 7 digits containing each of the digits 1, 2, 3, 4, 5, 6, 7 exactly once, and not divisible by 5 = 1X5X5X4X3X2X1 = 600
Starting with 3, total No. of 7 digits containing each of the digits 1, 2, 3, 4, 5, 6, 7 exactly once, and not divisible by 5 = 1X5X5X4X3X2X1 = 600
Total up to starting with 3, total No. of 7 digits containing each of the digits 1, 2, 3, 4, 5, 6, 7 exactly once, and not divisible by 5 = 600+600+600 = 1800
Starting with 41, total No. of 7 digits containing each of the digits 1, 2, 3, 4, 5, 6, 7 exactly once, and not divisible by 5 = 1X1X4X4X3X2X1 = 96
Starting with 42, total No. of 7 digits containing each of the digits 1, 2, 3, 4, 5, 6, 7 exactly once, and not divisible by 5 = 1X1X4X4X3X2X1 = 96
Total up to Starting with 42, total No. of 7 digits containing each of the digits 1, 2, 3, 4, 5, 6, 7 exactly once, and not divisible by 5 = 1800+96+96 = 1992
Starting with 431, total No. of 7 digits containing each of the digits 1, 2, 3, 4, 5, 6, 7 exactly once, and not divisible by 5 = 1X1X1X3X3X2X1 = 18
Total number is 1992+18 = 2010 which is more than 2000th digit
Starting with 4312, total No. of 7 digits containing each of the digits 1, 2, 3, 4, 5, 6, 7 exactly once, and not divisible by 5 = 1X1X1X1X2X2X1 = 4
Total number is 1992+4 = 1996 which is less than 2000th digit
Hence Starting with 4315 numbers of7 digits containing each of the digits 1, 2, 3, 4, 5, 6, 7 exactly once, and not divisible by 5 are
4315267, 4315276, 4315627, 4315672, 4315726, 4315762,
Already we got 1996 numbers. To get 2000th digit we have calculate more 4 numbers.
So 2000th digit is = 4315672
hope my answer is correct