2. A sweatshirt comes in 3 sizes and 8 colors. How many different sweatshirts are available.
There are 24 different sweatshirt options available (3 sizes x 8 colors).
There are 6 runners in the 100 meter race at a track meet. In how many ways can the runners be arranged?
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).
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?
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).
3. Simplify the expression ¹⁰P².
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.
Which expressions are equal to 120?
A. 5!
B. 6!
C. ⁶P³
D. ¹²P¹⁰
A. 5! = 120
Therefore, expression A is equal to 120.
To find out how many different sweatshirts are available, we can use the concept of combinatorics.
First, we need to multiply the number of sizes with the number of colors. In this case, there are 3 sizes and 8 colors. Multiplying these together gives us 3 * 8 = 24.
So, there are 24 different combinations of sizes and colors for the sweatshirt. Therefore, there are 24 different sweatshirts available.