A gentleman has 6 friends to invite, Inhow many ways can he send invitation cards to them, if he has threee servants to carry the cards?

Find the number of different words that can be formed from the letters of the word 'TRIANGLE' so that no vowels are together.

Find the number of ways in which a team of eleven players can be selected from 22 players, if two particular player are always including anf four are always excluding

Evaluate ¹⁵C₈ + ¹⁵C₉ -¹⁵C₆ -¹⁵C₇

Sunil wants to arrange 3 Economics, 2 History and 4 Language books on a shelf. If the books of the same subject are different.Determine the number of all possible arrangements

If ¹⁵C_r : ¹⁵C_r-1=11:5 Find r

A room has 7 doors. In how many ways can a man enter the room through one door and come out through a different door ?

The flag of a newly formed forum is in the form of three blocks \(\Box \Box \Box \), each to be coloured differently. If there are six different colours on the whole to choose from, how many such designs are possible ?

Evaluate the following: \(^{ 35 }{ C }{ _{0} }\)

Evaluate\(\frac { n! }{ (n-r)! } \)when r =3.

If \(^{n+2}{C}{_{8}}\) : \( ^{n-2}{P}{_{4}} \)= 57:16, then find the value of n.

Find the value of r, if ⁵P_r=2\(\times \)⁶P_r-1.

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?

Find the number of different 8 letters of the word 'DAUGHTER' so that all vowels do not occur together.

A box contains two white, three black and four red balls. In how many ways can three balls be drawn from the box, if atleast one black ball is to be included in the draw

How many different words can be formed with the letters of the word 'TRIANGLE' So that the word being with T and end with E.