The number of 6 digit numbers hat can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digits is repeated, is
(A) 36 (B) 60
(C) 72 (D) 48
Answers
48 Such numbers are possible which are divisible by 11
Step-by-step explanation:
The divisibility rule of eleven states that we must subtract and then add the digits in an alternating pattern from left to right; if the answer is 0 or 11 then the result is divisible by 11.
1 + 9 + 2 = 12
0 + 5 + 7 = 12
12 - 12 = 0
case 1 :
1 , 9 , 2 Take 1st 3rd 5th place
0 , 5 , 7 takes 2nd , 4th , 6th place
3! - 1st 3rd 5th place
3! - 2nd , 4th , 6th place
possible numbers = 3! * 3 !
= 6 * 6
= 36
Case 2 :
0 , 5 , 7 Take 1st 3rd 5th place
1 , 9 , 2 takes 2nd , 4th , 6th place
0 can not take 1st place
ist place 2 ways remaining 3rd 5th place 2!
2 * 2! = 1st 3rd 5th place
3! - 2nd , 4th , 6th place
possible numbers = 2 * 2 * 3! = 12
36 + 12 = 48
48 Such numbers are possible which are divisible by 11
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