1. 4!
a.) 3
b.) 6
c.) 12
d.) 24******
2. 5!
a.) 25********
b.) 120
c.) 250
d.) 625
5. Five friends are having their picture taken. How many ways can the photographer arrange the friends in a row?
a.) 150
b.) 100
c.) 120*******
d.) 80
6. How would you apply the fundamental counting principle to a bike lock combination with 5 numbers?
a.) 10 + 10 + 10 + 10 + 10
b.) 10 × 5
c.) 10 × 10 × 10 × 10 × 10*******
d.) none of these
Odd. you got 4! correct, but think 5! is 5^2?
And then you got #5 correct, too!
#6 ok as well.
1. To find the value of 4!, we need to calculate the factorial of 4. The factorial of a number is the product of all positive integers from 1 to that number. In this case, 4! = 4 x 3 x 2 x 1 = 24. Therefore, the correct answer is d.) 24.
2. Similar to the previous question, we need to calculate the factorial of 5. 5! = 5 x 4 x 3 x 2 x 1 = 120. Therefore, the correct answer is b.) 120.
3. When arranging the friends in a row, we are looking for the number of possible permutations. Since there are five friends, we have 5 choices for the first position, 4 choices for the second position (once the first friend is placed), 3 choices for the third position, 2 choices for the fourth position, and 1 choice for the last position. Therefore, the number of possible arrangements is 5 x 4 x 3 x 2 x 1 = 120. Therefore, the correct answer is c.) 120.
4. To apply the fundamental counting principle to a bike lock combination with 5 numbers, we need to determine the number of choices for each digit. In this case, the lock has 10 numbers (0-9) for each digit. Since there are 5 digits on the lock, we need to multiply the number of choices for each digit together. Therefore, the correct answer is c.) 10 x 10 x 10 x 10 x 10 = 100,000 combinations.