Home
Class 12
MATHS
The number of arrangments of all digits ...

The number of arrangments of all digits of `12345` such that at least `3` digits will not come in its position is

Text Solution

Verified by Experts

The correct Answer is:
109
Total number of ways such that at least 3 digits will not come in its position.
=Derangement of 3 digits +Derangement of 4 digits +Derangement of 5 digits
`= ""^(5)C_(3)xx3!xx(1-(1)/(1!)+(1)/(2!)-(1)/(3!))+""^(5)C_(4)xx4!xx(1-(1)/(1!)+(1)/(2!)-(1)/(3!)+(1)/(4!))+""^(5)C_(5)xx5!xx(1-(1)/(1!)+(1)/(2!)-(1)/(3!)+(1)/(4!)-(1)/(5!))`
`=10xx2+5xx9+44`
`=20+45+44=109`
Promotional Banner

Similar Questions

Explore conceptually related problems

The number of 5 digit numbers all digits of which are odd is

The number of nine nonzero digits such that all the digits in the first four places are less than the digit in the middle and all the digits in the last four places are greater than that in the middle is a. 2(4!) b. 3(7!)//2 c. 2(7!) d. ^4P_4xx^4P_4

The number of four-digit numbers that can be formed by using the digits 1,2,3,4,5,6,7,8 and 9 such that the least digit used is 4 , when repetition of digits is allowed is

The number of 4 digit natural numbers such that the product of their digits is 12 is

The number of n digit numbers which consists of the digit 1 and 2 only if each digit is to be used at least once is equal to 510, then n is equal to ________.

The number of five digit telephone numbers having at least one of their digits repeated is

The number of n digit number formed by using digits {1,2,3} such that if 1 appears, it appears even number of times, is

The number of five digit numbers in which all digits are even, is :