Ashley is packing her bags for her vacation. She has 7 unique socks, but only 3 fit in her bag.
How many different groups of 3 socks can she take?

There are 35 possible group of 3 socks from a total of 7

Step-by-step explanation:

Given

Number of unique socks = 7

Number of possible selection = 3

Required

Number of ways she can make her selection.

The question can be categorised as combination; reason being that words like "take" as used in the question points to combination or selection.

To solve this, we make use of combination formula.

nCr = nPr/r!

Where n = 7 and r = 3

By substitution, we have

7C3 = 7P3÷3!

Taking it one at a time

7P3 = 7!÷(7-3)!

7P3 = 7! ÷ 4!

7P3 = 7 * 6 * 5 * 4! ÷ 4!

7P3 = 7 * 6 * 5

7P3 = 210

3! = 3 * 2 * 1

3! = 6.

So,

7C3 = 210 ÷ 6

7C3 = 35.

Hence, there are 35 possible group of 3 socks from a total of 7

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3