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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