List of top Mathematics Questions on fundamental principle of counting

There are two main entrances to a building with five floors. Each entrance leads to three lifts and each lift can stop at all the five floors. A person enters the building and reaches a floor. The number of possible ways that the person can reach the floor, is

The total number of 4-digit numbers whose greatest common divisor with 54 is 2 , is ____.

The total number of 3-digit numbers, whose greatest common divisor with 36 is 2, is _______.

The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is

The total number of 7 digit positive integral numbers with distinct digits that can be formed using the digits 4, 3, 7, 2, 1, 0, 5 is:

How many four digit numbers \( abcd \) exist such that \( a \) is odd, \( b \) is divisible by 3, \( c \) is even and \( d \) is prime?

How many four digit numbers \( abcd \) exist such that \( a \) is odd, \( b \) is divisible by 3, \( c \) is even and \( d \) is prime?

How many four digit numbers \( abcd \) exist such that \( a \) is odd, \( b \) is divisible by 3, \( c \) is even and \( d \) is prime?

If \(\frac{1}{6!}+\frac{1}{7!}=\frac{x}{8!}\), find x.

Evaluate \(\frac{n!}{\left(n-r\right)!}\), when 
(i) n = 6, r = 2 (ii) n = 9, r = 5