Let us assume there are six seats.

In the first seat, any one of six members can be seated, so the total number of possibilities is ^{6}C_{1}

In the second seat, any one of five members can be seated, so the total number of possibilities is ^{5}C_{1} ways.

In the third seat, any one of four members can be seated, so the total number of possibilities is ^{4}C_{1} ways.

In the fourth seat, any one of three members can be seated, so the total number of possibilities is ^{3}C_{1} ways.

In the fifth seat, any one of two members can be seated, so the total number of possibilities is ^{2}C_{1} ways.

In the sixth seat, only one remaining person can be seated, so the total number of possibilities is ^{1}C_{1} ways.

Hence, the total number of possible outcomes = ^{6}C_{1} × ^{5}C_{1} × ^{4}C_{1} × ^{3}C_{1} × ^{2}C_{1} × ^{1}C_{1} = 6 × 5 × 4 × 3 × 2 × 1 = 720.

How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?

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

How many words, with or without meaning can be formed from the letters of the word ‘MONDAY’, assuming that no letter is repeated, if

**(i)** 4 letters are used at a time

**(ii)** all letters are used at a time

**(iii)** all letters are used but first letter is a vowel ?

There are 10 persons named P_{1}, P_{2}, P_{3} …, P_{10}. Out of 10 persons, 5 persons are to be arranged in a line such that is each arrangement P_{1} must occur whereas P_{4} and P_{5} do not occur. Find the number of such possible arrangements.

How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?