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

Sum

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

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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APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.4 | Q 13 | Page 83