The number of signals that can be sent by 6 flags of different colours
taking one or more at a time is
(A) 63
(B) 1956
(C) 720
(D) 21

In an examination there are three multiple choice questions and each
question has 4 choices. Number of ways in which a student can fail to get all answer correct is
(A) 11
(B) 12
(C) 27
(D) 63

Eight chairs are numbered 1 to 8. Two women and 3 men wish to occupy one chair each. First the women choose the chairs from amongst the chairs 1 to 4  and then men select from the remaining chairs. Find the total number of possible
arrangements.

If the letters of the word RACHIT are arranged in all possible ways as listed in dictionary. Then what is the rank of the word RACHIT?

A candidate is required to answer 7 questions out of 12 questions, which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. Find the number of different ways of doing questions.

Out of 18 points in a plane, no three are in the same line except five points which are collinear. Find the number of lines that can be formed joining the point.

We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can selections be made?

How many committee of five persons with a chairperson can be selected from 12 persons.

How many automobile license plates can be made if each plate contains two different letters followed by three different digits?

A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected from the lot.

Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.