Question

A wardrobe contains 3 blue, 4 green, and 3 red shirts; 2 blue, 4 green, and 6 red sweaters; 1 blue and 2 grey pants. Suppose blue and grey do not mix. How many outfits are possible? please answer in the fastest way possible without counting everything separately and adding after

Answer 1

Solution:

Given:

	Shirts	Sweaters	Pants
Blue	3	2	1
Green	4	4	0
Red	3	6	0
Grey	0	0	2
Totals	10	12	3

We have to find number of possible outfits such that Blue and Grey color do not mix.

First we will find All possible outfits.

Thus all possible outfits = 10 Shirts X 12 Sweaters X 3 Pants = 360

Now find number of outfits which consists of Blue and Grey color:

=3 Blue Shirts X 2 Blue Sweaters X 2 Grey Pants

+3 Blue Shirts X 4 Green Sweaters X 2 Grey Pants

+ 3 Blue Shirts X 6 Red Sweaters X 2 Grey Pants

+ 4 Green Shirts X 2 Blue Sweaters X 2 Grey Pants

+ 3 Red Shirts X 2 Blue Sweaters X 2 Grey Pants

=12+24+36+16+12

=100

Thus number of possible outfits such that Blue and Grey color do not mix = 360 - 100

Number of possible outfits such that Blue and Grey color do not mix = 260