Answer :
The number of 6-digit numbers divisible by 11, without repeated digits from 0,1,2,5,7,9, is 40.
To find the number of 6-digit numbers that can be formed using the digits 0, 1, 2, 5, 7, and 9, and are divisible by 11 with no digit repetition, we employ the divisibility rule for 11. This rule stipulates that the difference between the sum of digits at odd places and even places should be a multiple of 11 or zero.
Given the digit set, arranging them to satisfy the divisibility by 11 is limited. Starting with the hundreds place, two possibilities exist: (0, 5, 7) or (1, 2, 9). The tens and units places allow any order without repetition, resulting in [tex]\(2 \times 5 \times 4\)[/tex] possibilities for the entire 6-digit number.
Consequently, the total count of 6-digit numbers meeting the criteria is [tex]\(2 \times 5 \times 4 = 40\).[/tex]
In conclusion, there are 40 distinct 6-digit numbers that can be formed using the specified digits, satisfying the conditions of divisibility by 11 and absence of repeated digits.
The question probable may be:
The number of 6 digit numbers that can be formed using the digits 0,1,2,5,7 and 9 which are divisible by 11 and no digit is repeated, would be?
