How many 2 digit even numbers can be formed from the digits 1, 2, 3, 4, 5 if the digits can be repeated?

How many 4-digit numbers are there, when a digit may be repeated any number of times?

Find the number of triangles thet are formed by choosing the vertices from a set of 10 points 6 of which lie on the same line

How many different signals can be made by 5 flags from 8 flags of different colours?

Find x, if \({1\over 7!}+{1\over 8!}={x\over 9!}\)

Evaluate the following:\(^{ 14 }{ C }{ _{ 3 } } \)

Everybody in a room shakes hands with everybody else. The total number of Hand-shakes is 66. Find the total number of persons in the room.

Find the LCM of \(6!,7!\) and \(8!\). 

A man has 7 friends . In how many ways can he one or more them to party?

If  ⁸C_r  - ⁷C₃ = ⁷C₂ , Find r

How many natural numbers less than 1000 can be formed with the digits 1, 2, 3, 4, and 5, if repetition of digits is allowed?

How many different words can be formed with the letters of the word 'HARYANA'? How many of these begin with H and end with N?

Find the total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants.

In how many ways a committee of 3 men and 2 women can be chosen fronm 7 men and 5 women ?

From among the 35 teachers in aschool, one pricipal and one vice principal  are to be appointed. In how many ways can this be done?

In how many ways can the letters of the word PERMUTATIONS be arranged if the
(i) words start with P and end with S
(ii) vowels are all together
(iii) there are always 4 letters between P and S?