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In his suitcase, Jack has 3 shirts, 4 pants, 2 socks (pairs of socks), and 2 shoes (pairs of shoes). How many unique ways can Jack get fully dressed? Show your work and explain.

Explanation:

Use the counting principle. Let's say we had a table where it has 3 rows to represent the number of shirts Jack has. Then lets make this table have 4 columns to represent the number of pants. So far, Jack has 3*4 = 12 different outfits if we just focus on shirts and pants only. This is the exact same as the number of cells in this 3 by 4 table.

This can be extended further to any number of items and not just two types. A tree diagram is sometimes handy to show all the various possibilities. Though the more items you have, the messier it gets.

The summary is that we just multiply out the numbers given:

So Jack has 3*4*2*2 = 12*4 = 48 different outfits.

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1