Discussion
In how many ways can a lady having 10 dresses, 5 pairs of shoes, and 2 hats be dressed ?
Answer: B
She can be dressed in 100 ways.
Choosing an outfit is three independent choices made one after another: a dress (10 ways), a pair of shoes (5 ways) and a hat (2 ways). By the multiplication principle,
\[ 10 \times 5 \times 2 = 100 \]
The figure 50 forgets the hats, and 500 multiplies by an extra factor of 5. The expression 10!5!2! counts orderings of all the items within each type, which has nothing to do with choosing one of each.
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