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  4. The number of natural numbers lying between 1012 and 23421 that can be formed using the digits 2,3, 4, 5, 6 (repetition of digits is not allowed) and divisible by 55 is

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Q. The number of natural numbers lying between 1012 and 23421 that can be formed using the digits 2,3, 4, 5, 6 (repetition of digits is not allowed) and divisible by 55 is

JEE MainJEE Main 2022Permutations and Combinations

Solution:

4 digit numbers
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$a+c=b+5 $
$\text { for } b=1 a=2, c=4 $
$ a=4, c=2$
$\text { for } b=2 a=3, c=4$
$ a=4, c=3$
$\text { for } b=3 a=6, c=2 $
$ a=2, c=6$
$\therefore 6$ possible four digit no.s are div. by 55
(II) 5 digit number is not possible

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