.
In all, there are = = 462 ways to form group of 5 from 11 items (persons).
Of them, those groups are prohibited (and must be subtracted from 462) that contain these two special friends.
So we need to count the number of such groups.
The number of such groups is exactly the number of ways you can complement these two special persons to the group of 5,
by adding 3 other persons from 11-2 = 9 remaining.
You can do it in = = 84 ways.
So, the answer to the problem question is this difference
462 - 84 = 378.
Solved.
-------------------
On Combinations, see the lessons
- Introduction to Combinations
- PROOF of the formula on the number of Combinations
- Problems on Combinations
- OVERVIEW of lessons on Permutations and Combinations
in this site.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Combinatorics: Combinations and permutations".
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.