# Counting Principle Worksheet

Counting Principle Worksheet
• Page 1
1.
Find the number of choices available to choose an animal in the tree diagram.

 a. 9 b. 12 c. 18 d. 14

2.
Which of the tree diagrams represents all the possible outcomes of tossing two coins?

 a. Figure 1 b. Figure 2 c. Figure 3 d. Figure 4

3.
Use the tree diagram to find the number of ways in which Paul can choose a tie.

 a. 2 b. 3 c. 9 d. 6

4.
A blue, red or green cube is selected and a coin is tossed. Which of the tree diagrams represents all the possible outcomes of the two events?

 a. Tree diagram 1 b. Tree diagram 2 c. Tree diagram 3 d. Tree diagram 4

5.
A 3-digit number is formed with the digits 1, 2, 3, 4, 5, 6 with no repetition of any digit. Find the probability that the number is divisible by 5.
 a. 1 b. $\frac{5}{6}$ c. $\frac{1}{2}$ d. $\frac{1}{6}$

6.
3 persons attend an interview at a company where each person can be either selected or rejected. Find the number of ways of announcing the result.
 a. 2 b. 8 c. 4 d. 16

7.
There are 5 routes from City A to City B, 9 routes from City B to City C. Find the number of different ways for a person to travel from City A to City C via City B.
 a. 44 b. 14 c. 46 d. 45

8.
From a group of 14 children, 11 boys and 3 girls, 3 children are selected at random. Find the probability that the selected group contains more girls than boys.
 a. $\frac{381}{182}$ b. $\frac{563}{182}$ c. $\frac{17}{182}$ d. $\frac{199}{182}$

 a. $\frac{\left({}_{20}{C}_{2}\right)\left({}_{10}{C}_{3}\right)}{{}_{45}{C}_{8}}$ b. $\frac{3}{8}$ c. $\frac{\left({}_{15}{C}_{3}\right)\left({}_{20}{C}_{2}\right)\left({}_{10}{C}_{3}\right)}{{}_{45}{C}_{8}}$ d. $\frac{\left({}_{15}{C}_{8}\right)}{{}_{45}{C}_{8}}$