(1) From the information given, if we want to choose 5 colors from 8 distinct colors and the order in which the selection is made is relevant, then what we have is a permutation.
The formula is given as;

This formula means we need to select/arrange r items out of a total of n items and the anwer derived would be the total number of arrangements possible.
Therefore, we would have;

Therefore, if the order is relevant, this selection can be done in 6,720 ways.
(2) If the order is NOT relevant, then what we need to calculate is a combination and the formula is;

The formula can now be applied as follows;

If the order is not relevant, then the selection can be done in 56 ways.
Each teacher has 25 students. 75/3 would be 25. I hope this helped!
Answer:
{9,14,20}
Step-by-step explanation:
hope it helps
Use the change-of-basis identity,

to write

Use the product-to-sum identity,

to write

Redistribute the factors on the left side as

and simplify to

Now expand the right side:

Simplify and rewrite using the logarithm properties mentioned earlier.





(C)
Answer:
1. -7/8
2.-9/14
3. 9/14
4. 7/8
2. what is the product of -2/7 and -3/7?
1. -7/8
2.-6/49
3. 6/49
4. 7/8
How do the expressions 72÷ 9 and -72÷ (-9) compare when they are evaluated?
1. They have different values and are different signs.
2. They have different values but are the same sign.
3. They have the same value but are different signs.
4. They have the same value and the same sign.
Step-by-step explanation:
Multiplying fractions: multiply numerators and multiply denominators
1. 3/4 X -6/7 = -18/28 = -9/14
2. -2/7 X -3/7 = 6/49
3. 4 because 72/9 is 8. -72/-9 is 8. Two negatives makes a positive when multiplying and dividing.