Wiley Edge Permutations and Combination Quiz-3

Explanation:
The number of ways to choose one appetizer, one main course, and one dessert can be calculated by multiplying the number of choices for each category.
Number of ways to choose one appetizer = 12.
Number of ways to choose one main course = 8.
Number of ways to choose one dessert = 5.
Total number of ways to choose the meal = 12 * 8 * 5 = 480.

Explanation:
For the first dial, we have 9 choices (1 to 9, excluding 0).
For the second dial, we have 9 choices (0 to 9, excluding first dial choice).
For the first dial, we have 8 choices (0 to 9, excluding first and second dial).
For the first dial, we have 7 choices (0 to 9, excluding first ,second and third dial).
Therefore, the total number of combinations = 9 * 9 * 8 * 7 = 4536.

Answer: 1,680
Explanation:
The number of ways to choose 3 managers from 8 and 2 employees from 6 can be calculated using the combination formula:
Number of ways to choose 3 managers = C(8, 3) = 8! / (3! * (8-3)!) = 56.
Number of ways to choose 2 employees = C(6, 2) = 6! / (2! * (6-2)!) = 15.
Total number of ways to form the committee = Number of ways to choose 3 managers * Number of ways to choose 2 employees
=> 56 * 15
=> 1,680

Answer: 0.028
Explanation:
The total number of ways to draw 5 tickets out of 100 is given by C(100, 5) = 75,287,520.
The number of ways to draw 5 tickets with all odd numbers is given by C(50, 5) = 2,118,760 (selecting 5 tickets out of the 50 odd-numbered tickets).
Therefore, the probability = 2,118,760 / 75,287,520
≈ 0.0282
≈ 0.028

Answer: 445
Explanation:
To calculate the number of ways to choose 3 balls with at least one red ball, subtract the number of ways to choose 3 blue balls from the total number of ways to choose 3 balls.
Number of ways to choose 3 blue balls = C(5, 3) = 5! / (3! * (5-3)!) = 10.
Total number of ways to choose 3 balls = C(15, 3) = 15! / (3! * (15-3)!) = 455.
Number of ways to choose 3 balls with at least one red ball = Total number of ways to choose 3 balls - Number of ways to choose 3 blue balls
=> 455 - 10
=> 445

Answer: 1680
Explanation:
The word "ARTICLES" has 8 letters, so there are 8 choices for the first letter, 7 choices for the second letter, 6 choices for the third letter, and 5 choices for the fourth letter.
Therefore, the total number of different 4-letter words = 8 * 7 * 6 * 5 = 1,680.

Answer : 15
Explanation :
There are 3 options for the pizza size and 5 options for the toppings. Since we need to choose one size and at least one topping, the total number of pizzas can be calculated by multiplying the number of options for size by the number of options for toppings: 3 * 5 = 15.

Answer: 15120
Explanation:
The word "BACKFLOWS" has 9 letters, so there are 9 choices for the first letter, 8 choices for the second letter, 7 choices for the third letter, 6 choices for the fourth letter and 5 choices for the fifth letter.
Therefore, the total number of different 4-letter words =9 * 8 * 7 * 6 * 5 = 15,120.

Answer: 720
Explanation:
xBxBxBxBxBx
Ways in which boys can be arranged = 5! = 120
Ways in which Girls can be arranged = C(6,5) = 6
Total Number of Ways = 120 * 6 = 720

Answer: 5040
Explanation:
Treat Atulya and Manish as a single entity. Now, we have 7 entities (Atulya and Manish together and the other 6 people) to arrange in a row. The number of ways to arrange these entities is 7!, which is equal to 5040.