2. A sweatshirt comes in 3 sizes and 8 colors. How many different sweatshirts are available.

Answer 1

There are 24 different sweatshirt options available (3 sizes x 8 colors).

Answer 2

There are 6 runners in the 100 meter race at a track meet. In how many ways can the runners be arranged?

Answer 3

There are 720 different ways the runners can be arranged (6 factorial, or 6! which is 6 x 5 x 4 x 3 x 2 x 1).

Answer 4

Dave has work shirts in 5 different colors. He works three days each week. How many possible arrangements are there for the shirts each week?

Answer 5

There are 125 different possible arrangements for Dave's work shirts each week (5 colors to choose from for each of the 3 days, so 5 x 5 x 5 = 125).

Answer 6

3. Simplify the expression ¹⁰P².

Answer 7

Using the formula for permutations:

nP r = n! / (n-r)!

Here, n = 10 and r = 2.

So,

10P2 = 10! / (10-2)!
= 10! / 8!
= 10 x 9
= 90

Therefore, ¹⁰P² = 90.

Answer 8

Which expressions are equal to 120?

A. 5!

B. 6!

C. ⁶P³

D. ¹²P¹⁰

Answer 9

A. 5! = 120

Therefore, expression A is equal to 120.