PERMUTATIONS AND COMBINATIONS PERMUTATIONS AND COMBINATIONS Let us name the three pants as P , P , P and the two shirts as S , S . Then, these six possibilities can be illustrated in the Fig. . .
Let us consider another problem of the same type. Sabnam has school bags, tiffin boxes and water bottles. In how many ways can she carry these items (choosing one each). A school bag can be chosen in different ways.
After a school bag is chosen, a tiffin box can be chosen in different ways. Hence, there are × = pairs of school bag and a tiffin box. For each of these pairs a water bottle can be chosen in different ways. Hence, there are × = different ways in which, Sabnam can carry these items to school.
If we name the school bags as B , B , the three tiffin boxes as T , T , T and the two water bottles as W , W , these possibilities can be illustrated in the Fig. . . Fig .
Fig . MATHEMATICS In fact, the problems of the above types are solved by applying the following principle known as the fundamental principle of counting , or, simply, the multiplication principle , which states that “If an event can occur in m different ways, following which another event can occur in n different ways, then the total number of occurrence of the events in the given order is m×n.” The above principle can be generalised for any finite number of events. For example, for events, the principle is as follows: ‘If an event can occur in m different ways, following which another event can occur in n different ways, following which a third event can occur in p different ways, then the total number of occurrence to ‘the events in the given order is m × n × p .” In the first problem, the