Question

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

Answer 1

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.