Select Page

# Combinatorics

Tagged:

Viewing 2 posts - 1 through 2 (of 2 total)
• Author
Posts
• #70881
Shreya Nair
Participant

Is the solution correct?

###### Attachments:
You must be logged in to view attached files.
#74639
Shirsendu Roy
Moderator

There are 4 even numbers and 4 odd numbers

if an even and odd number is paired then no pair of gcd 2

which is 4!=24 ways.

the order of odd numbers can be shuffled that many different ways in each case pairing the first odd number with 2, the second one with 4, and so on.

if even and odd are not paired then

two even numbers is paired

here the pair of even numbers in the set that have gcd not 2 is 4 and 8.

so pair of 4 and 8 taken.

choose two odd numbers to pair together in {4 \choose 2}=6 different ways and pair the remaining two odd numbers in 2 different ways with 2 and 6

which gives (2)(6)=12 different ways

so two methods give 24+12=36 ways.

Viewing 2 posts - 1 through 2 (of 2 total)
• You must be logged in to reply to this topic.