The letter of the word LABOUR are permuted in all possible ways and the words thus formed are arranged as in a dictionary. What is the rank of the word LABOUR?

A class photograph has to be taken. The front row consists of 6 girls who are sitting. 20 boys are standing behind. The two corner positions are reserved for the 2 tallest boys. In how many ways can the students be arranged?

If $$5{ \times ^{\text{n}}}{{\text{P}}_3} = 4{ \times ^{\left( {{\text{n}} + 1} \right)}}{{\text{P}}_{3,}}$$    find n?

Ten different letters of alphabet are given, words with 5 letters are formed from these given letters. Then, the number of words which have at least one letter repeated is:

12 chairs are arranged in a row and are numbered 1 to 12. 4 men have to be seated in these chairs so that the chairs numbered 1 to 8 should be occupied and no two men occupy adjacent chairs. Find the number of ways the task can be done.

How many words can be formed by re-arranging the letters of the word ASCENT such that A and T occupy the first and last position respectively?

If 6Pr = 360 and If 6Cr = 15, find r ?

In how many ways can six different rings be worn on four fingers of one hand?

There are 7 non-collinear points. How many triangles can be drawn by joining these points?

From 6 men and 4 ladies, a committee of 5 is to be formed. In how many ways can this be done, if the committee is to include at least one lady?

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