Spoilt for choice...
Brenda has 3 blouses, 4 dresses, 1 pair of shorts, 2 pairs of pants and 2 skirts. For her innerwear, she has 3 bras and 4 pairs of knickers. In how many ways can she dress?
Details and assumptions:
-
Brenda has to wear both types of innerwear.
-
She only wears one layer of outer clothing on both her upper and lower body.
The answer is 228.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Since Brenda has to wear both types of innerwear, there are 3 × 4 = 1 2 possible combinations by Multiplication Principle.
As for her outerwear, there are 2 scenarios we need to consider - she can dress in one-piece or in two pieces. If she dresses in one piece, there are 4 possibilities (the number of dresses she has since her dresses are her only clothing in one piece).
If she dresses in 2 pieces, the number of possibilities is the number of topwear (blouses) she has multiplied by the number of bottomwear (shorts, pants, skirts) she has which is 3 × ( 1 + 2 + 2 ) = 3 × 5 = 1 5 . For her outerwear, there are 1 5 + 4 = 1 9 possibilities by addition principle.
By multiplication principle, there are a total of 1 9 × 1 2 = 2 2 8 ways.