required number of ways of wearing a pant and a shirt was the number of different ways of the occurence of the following events in succession: the event of choosing a pant the event of choosing a shirt. In the second problem, the required number of ways was the number of different ways of the occurence of the following events in succession: the event of choosing a school bag the event of choosing a tiffin box (iii) the event of choosing a water bottle. Here, in both the cases, the events in each problem could occur in various possible orders. But, we have to choose any one of the possible orders and count the number of different ways of the occurence of the events in this chosen order.
Example Find the number of letter words, with or without meaning, which can be formed out of the letters of the word ROSE, where the repetition of the letters is not allowed. Solution There are as many words as there are ways of filling in vacant places by the letters, keeping in mind that the repetition is not allowed. The first place can be filled in different ways by anyone of the letters R,O,S,E. Following which, the second place can be filled in by anyone of the remaining letters in different ways, following which the third place can be filled in different ways; following which, the fourth place can be filled in way.
Thus, the number of ways in which the places can be filled, by the multiplication principle, is × × × = . Hence, the required number of words is . PERMUTATIONS AND COMBINATIONS