The flag of a newly formed political party is to be in the form of the three blocks, each of a different colour. If there are six distinct colours on the whole to choose from, find the number of all possible designs for the flags?

It has been decided that the flag of a newly formed forum will be in the form of three blocks, each coloured differently. If there are six colours on the whole to choose from, how many designs are possible ?

Each of the six squares in the strip shown in the fig., is to be coloured with anyone of ten different colours so that no two adjacent squares have the same colour. Find the number of ways of colouring the strip.

How many different signal can be giving using any number of flag from flag 4 of the different colour

How many different signals can be generated from 6 flags of different colours if each signal makes use of all the flags at a time, placed one below the other?

The ages of the students of a class form an A.P. whose common difference is 4 months. If the youngest student is 8 years old and the sum of the ages of all the students of the class 1s 168 years, find the number of students in the class.

Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?

The management committee of a residential colony decided to award some of its members (say x) for honesty, some (say y) for helping others and some other (sayz) for supervising the workers to keep the colony neat and clean. The sum of all the awardees is 12. Three times the sum of the awardees for cooperation and supervision added to two times the number of awardees for honesty is 33. If the sum of the number of awardees for honesty and supervision is twice the number of awardees for helping others. Using matrix method, find the number of awardees of each category, Apart form these values, namely honesty, cooperation and supervisio, suggest one more value, which the management of the colony must include for award.

Form the pair of linear equations In the following problems and find their solutions (if they exist) by any algebraic method. :- Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars ?