Sum

How many different 6-digit numbers can be formed using digits in the number 659942? How many of them are divisible by 2?

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#### Solution

A 6-digit number is to be formed using digits of 659942, in which 9 repeats twice.

∴ Total number of arrangements = `(6!)/(2!)`

= `(6 xx 5 xx 4 xx3 xx 2!)/(2!)`

= 360

∴ 360 different 6-digit numbers can be formed.

For a number to be divisible by 2,

Last digits can be selected in 3 ways

Remaining 5 digits in which, 9 appears twice are arranged in `(5!)/(2!)` ways

∴ Total number of arrangements

= `(5!)/(2!)xx3` = 180

∴ 180 numbers are divisible by 2.

Concept: Permutations When All Objects Are Not Distinct

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