BITSAT 2024 Shift 1 Paper

To find the number of ways to arrange 10 friends at dinner on two round tables, one with 4 people and the other with 6 , follow these steps:
Divide into Groups:
You need to create two groups from 10 people: one group with 4 people and another with 6 people.
The number of ways to form these groups is given by the combination formula:
‌

10!

4!×6!

Arrange on Round Tables:
Arranging 4 people on a round table can be done in (4−1) ! ways (since arrangements around a circle account for rotations being identical):
3 !
Arranging 6 people on a round table can be done in (6−1) ! ways:
5!
Total Arrangements:
Multiply the number of ways to form the groups by the number of ways to arrange each group on their respective tables:
‌

10!

4!×6!

×3!×5!
Simplifying, this expression calculates to:
‌

10!

24

Hence, the total number of ways to arrange the guests is ‌

10!

24

.