Ali's dining room table is round and has a radius of 4.5 ft. What is the tabletop's area? Use 3.14 for pi.
2 answers:
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Answer:
- A)
.
- B)
.
- C)
.
Step-by-step explanation:
All marbles here are identical. Also, the question isn't concerned about the order in which the marbles are drawn. Thus, all calculations here shall be combinations rather than permutations.
<h3>A)</h3>How many ways to choose three out of six identical red marbles without replacement?
.
Note that these three expressions are equivalent. They all represent the number of ways to choose 3 out of 6 identical items without replacement.
How many ways to choose three out of all the 6 + 10 + 6 = 22 marbles?
.
The probability of choosing three red marbles out of these 22 marbles will be:
.
How many ways to choose two out of six identical red marbles without replacement?
.
How many ways to choose one out of 10 + 6 = 16 non-red marbles?
.
Choosing two red marbles does not influence the number of ways of choosing a non-red marble. Both event happen and are independent of each other. Apply the product rule to find the number of ways of choosing two red marbles and one non-red marble out of the pile of 22.
.
Probability:
.
Double check that the order doesn't matter here.
<h3>C)</h3>None of the marbles are red. In other words, all three marbles are chosen out of a pile of 10 + 6 = 16 white and blue marbles. Number of ways to do so:
.
Probability:
.