Question: In how many ways can 5 people from a group of 8 people be seated around a circular table?

Solution:

5 people out of 8 = 8C5

= 8!/5!(8 - 5)!

= 8!/(3! × 5!)

​= (8 × 7 × 6 × 5!)/(6 × 5!)

= 56

And 5 people around a circular table = (5 - 1)! = 4! = 24

∴ Total ways = 24 × 56 = 1344

প্রশ্ন: 12 + 22 + 32+...............+ x2 এর মান কত?

সমাধান: 
আমরা জানি,
x সংখ্যক স্বাভাবিক সংখ্যার সমষ্টি = x(x + 1)/2
আবার
প্রথম x সংখ্যক স্বাভাবিক সংখ্যার বর্গের সমষ্টি = x(x + 1)(2x + 1)/6
12 + 22 + 32+...............+ x2 = x(x + 1)(2x + 1)/6

Question: If A = 2, B = 4, C = 6, D = 8, E = 10 and so on, what is the meaning of following number 40, 18, 14, 10, 36

Solution:
Given,
A = 2, B = 4, C = 6, D = 8, E = 10.......

∴ Each code = Letter position × 2

So
40 ÷ 2 = 20 → T
18 ÷ 2 = 9 → I
14 ÷ 2 = 7 → G
10 ÷ 2 = 5 → E
36 ÷ 2 = 18 → R

the meaning of following number = TIGER