Flag 10 grade maths> All possible numbers are formed using the...
question mark

All possible numbers are formed using the digits 1,1,2,2,2,2,3,4,4 taken all at a time. The number of such numbers in which the odd digits occupy even places is:






Aniket Singh , 5 Months ago
Grade
anser 1 Answers
Askiitians Tutor Team

Last Activity: 5 Months ago

To find the number of numbers that can be formed using the digits
1
,
1
,
2
,
2
,
2
,
2
,
3
,
4
,
4
1,1,2,2,2,2,3,4,4 where the odd digits (1, 3) occupy even places (2nd, 4th, 6th, etc.), you can follow these steps:

First, let's calculate the total number of permutations of all the digits. There are 9 digits in total, but some of them are repeated. You can calculate this using permutations with repetition:

Total permutations = 9! / (2! * 4!) = 9 * 8 * 7 * 6 * 5 * 4! / (2 * 4!) = 9 * 8 * 7 * 6 / 2 = 1512

Now, let's consider the even places (2nd, 4th, 6th, etc.) where odd digits (1, 3) need to be placed. There are 4 even places, and you have 2 odd digits (1, 3) to choose from.

Number of ways to choose the even places for odd digits = C(4, 2) = 6

For each of these combinations of even places, you can arrange the odd digits (1, 3) among themselves in 2! ways.

Number of ways to arrange odd digits = 2!

For the remaining places (1st, 3rd, 5th, etc.), you have the even digits (2, 2, 2, 2, 4, 4) to choose from, which can be arranged in
6
!
6! ways. However, the digit 2 appears four times and the digit 4 appears twice, so you need to account for the permutations of these repeated digits:

Number of ways to arrange even digits =
6
!
6! / (
4
!
4! *
2
!
2!)

Now, you can calculate the total number of numbers where odd digits occupy even places:

Total numbers = (Number of ways to choose even places for odd digits) * (Number of ways to arrange odd digits) * (Number of ways to arrange even digits)

Total numbers = 6 * 2! * (
6
!
6! / (
4
!
4! *
2
!
2!))

Calculate this expression to find the total number of such numbers where odd digits occupy even places.

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments