List of top Mathematics Questions on fundamental principle of counting asked in KEAM

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 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?