Question

6. In how many ways can a committee of 3 people be chosen out of 8 people?
7 A coin is rolled thrice, what is the event that two heads occur?.
8 What is the number of possible outcomes assumed to be equally likely if a coin is tossed thrice?.
9 Write down the sample space for a box containing 6 items of which 2 are defective. One item is chosen one after the other without replacement until the last defective item is chosen.
10 In how many ways can 12 objects be split into three groups containing 2,4 and 6 objects?

Answer 1

Answer on Question #59917 – Math – Statistics and Probability

Question

6. In how many ways can a committee of 3 people be chosen out of 8 people?

Solution

Using the formula of the number of combinations we obtain $C_8^3 = \frac{8!}{3! \cdot 5!} = 56$.

**Answer:** 56 ways.

Question

7. A coin is rolled thrice, what is the event that two heads occur?

**Answer:** The required event has the next form: $\{HHT, HTH, THH\}$, where $H$ is head, and $T$ is tail.

Question

8. What is the number of possible outcomes assumed to be equally likely if a coin is tossed thrice?

Solution

The possible outcomes are $\{HHH, HHT, HTH, THH, TTT, TTH, THT, HTT\}$. There are 8 outcomes.

**Answer:** 8.

Question

9. Write down the sample space for a box containing 6 items of which 2 are defective. One item is chosen one after the other without replacement until the last defective item is chosen.

Solution

Let $N$ be the non-defective item, and $D$ be the defective item. Then the sample space has the next form:

$DD, NDD, DND, NNDD, NDND, DNND, NNNDD, NNDND, NDNND, DNNND, NNNNDD, NNNDND, NNDNND, NNDNND, NNNNDND, NNNNDND, NNNNDND, NNNNNND, NNNNNND, NNNNNND, NNNNNND, NNNNNND, NNNNNND, NNNNNND, NNNNNNDD$.

Question

10. In how many ways can 12 objects be split into three groups containing 2, 4 and 6 objects?

Solution

Using the formula of the number of combinations and the formula of multiplication we obtain: $C_{12}^2 \cdot C_{10}^4 \cdot C_6^6 = \frac{12!}{2! \cdot 10!} \cdot \frac{10!}{4! \cdot 6!} \cdot 1 = 13860$ .

Answer: 13860 ways.

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