Question 2:- How many ways 6 Boys & 6 Girls batch students can be seated around a circular table such that no two boys are together.
Solution:- If one boys sit in the circle then the other student sit like a in linear
then, Number of arrangement of 6 Boys in circle = (6-1)! = 5!
Now, the girls will sit between the boys
then, the number of students can be seated around a circular table such that no two boys are together
= 5!×6! = 86,400 ways
Question 1:- Let S be the set of all passwords which are six to eight characters long, where each character is either an alphabet from {A, B, C, D, E} or a number {1, 2, 3, 4, 5} with the repetition of characters allowed. If the number of passwords in S whose at least one character is a number from {1, 2, 3, 4, 5} is 
, then α is equal to
Solution:- See full solution