প্রশ্ন: ৫ জন ব্যাক্তিকে একটি গোল টেবিলে কতভাবে বসানো যাবে?

সমাধান:

আমরা জানি,

n সংখ্যক ব্যক্তিকে একটি গোল টেবিলে বসানো যাবে = (n - ১)! উপায়ে 

 ৫ জন ব্যক্তিকে গোল টেবিলে বসানো যাবে = (৫ - ১)!

= ৪!

= ২৪ উপায়ে

Question: How many words can be formed by using the letters from the word 'DRIVER' such that all the vowels are never together?

Solution:
We assume all the vowels to be a single character, i.e., 'IE' is a single character.
So, now we have 5 characters in the word, namely, D, R, V, R, and IE.

But, R occurs 2 times.
Number of possible arrangements = 5!/2! = 60

Now, 
​the two vowels can be arranged in 2! = 2 ways.

Total number of possible words such that the vowels are always together = 60 × 2 = 120

Total number of possible words = 6!/2! = 720/2 = 360

Therefore, the total number of possible words such that the vowels are never together = 360 - 120 = 240

Question: Fifteen distinct points are randomly placed on the circumference of a circle. At most how many triangles can be formed using these points?
​
​Solution:
​Given that,
​Number of distinct points = 15
​Maximum number of triangles = 15C3
​= 15!/3!(15 - 3)!
​= (15 × 14 × 13 × 12!)/(3 × 2 × 12!)
= 455