combinatorics

How many integers are there between 100 and 1000 all of whose digits are even?

Arun, Gulab, Neel and Shweta must choose one shirt each from a pile of four shirts coloured red, pink, blue and white respectively. Arun dislikes the colour red and Shweta dislikes...

An e-mail password must contain three characters. The password has to contain one numeral from 0 to 9, one upper case and one lower case character from the English alphabet. How ma...

Candidates were asked to come to an interview with $$3$$ pens each. Black, blue, green and red were the permitted pen colours that the candidate could bring. The probability that a...

A box contains $$4$$ white balls and $$3$$ red balls. In succession, two balls are randomly selected and removed from the box. Given that first removed ball is white, the probabili...

Assume for simplicity that $$N$$ people, all born in April (a month of $$30$$ days) are collected in a room, consider the event of at least two people in the room being born on the...