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Explain principle of multiplication with an example.

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The multiplication principle says that the number of
ways in which the whole task can be performed is n1.n2....nk.
Let us consider this principle in the context of boxes and objects filling them. Suppose
there are m boxes. Suppose the first box can be filled up in k(1) ways. For every way
of filling the first box, suppose there are k(2) ways of filling the second box. Then the
two boxes can be filled up in k(1).k(2) ways. In general, if for every way of filling the
first (r − 1) boxes, the rth box can be filled up in k(r) ways, for r = 2,3,..., m, then the
total number of ways of filling all the boxes is k(1).k(2)... k(m).
So let us see how the multiplication principle can be applied to the situation above
(the shop selling pants). Here k(1) = 6, k(2) = 8, k(3) = 6 and k(4) = 4. So, the
different kinds of pants are 6 × 8 × 6 × 4 = 1152 in number.


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