Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • If the total number of ways in which 8-digit numbers can be formed by using all the digits 0,1,2,3,4,5,7,9 such that no two even digits appear together is (5!)k, then k is equal to:<

If the total number of ways in which 8-digit numbers can be formed by using all the digits 0,1,2,3,4,5,7,9 such that no two even digits appear together is (5!)k, then k is equal to:

Option: 1

100


Option: 2

42


Option: 3

30


Option: 4

12


Answers (1)

best_answer

Digit  0,1,2,3,4,5,7,9.

Odd = 1, 3, 5, 7, 9 

_O_O_O_O_O_

Five odd (O) places can be filled by digits  1, 3, 5, 7, 9 in 5! Ways

Now, 0, 2, 4 can be places in these 6 gaps. This can be done in 6C3 . 3! ways.

But out of these we will have to remove the ones where 0 lies at first place (as these numbers will not be 7-digit numbers)

So, put 0, at first place, then 2 and 4 can be placed in remaining 5 gaps in 5C2 . 2! ways

So, total number of ways = 5! ( 6C3 . 3! - 5C2 . 2!) = 5!(100)

k = 100

Posted by

HARSH KANKARIA

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions