Permutations & Combinations

Calculate the number of ways to arrange the letters in the word 'MISSISSIPPI' using permutations with repetition.

• 24,650

• 30,000

• 40,000

• 34,650

Explain the difference between permutations and combinations with an example.

• Permutations involve arranging objects in a specific order, while combinations involve selecting objects without considering the order.

• Permutations and combinations are the same concept with different names.

• Permutations involve selecting objects without considering the order, while combinations involve arranging objects in a specific order.

• Permutations involve selecting objects with a specific order, while combinations involve selecting objects without any order.

In a group of 5 students, how many ways can a president, vice president, and treasurer be selected using permutations?

• 120

• 30

• 10

• 60

Calculate the number of ways to arrange the letters in the word 'MATH' without repetition.

• 6

• 12

• 24

• 18

When would you use permutations instead of combinations in a real-life scenario? Provide an example.

• When the order of elements doesn't matter, like selecting a committee.

• When you are interested in the total number of ways to select items, not the specific order.

• When the order of elements matters, such as arranging a playlist of songs.

• When you need to choose a subset of items without repetition, such as picking lottery numbers.

A lock has 4 digits, each ranging from 0-9. How many possible combinations are there for the lock?

• 9999

• 1234

• 0000

• 10000

In a deck of 52 cards, how many ways can you choose 5 cards to form a poker hand using combinations?

• 2,598,960

• 3,456,789

• 1,234,567

• 5,678,901

Explain a scenario where both permutations and combinations are used together to solve a problem.

• Permutations are used to calculate the total number of ways to arrange the selected members in a specific order, while combinations are used to calculate the total number of ways to select the committee without considering the order of selection.

• Permutations are used to calculate the total number of ways to arrange the selected members in a specific order, while combinations are used to calculate the total number of ways to select the committee considering the order of selection.

• Permutations are used to calculate the total number of ways to select the committee without considering the order of selection, while combinations are used to calculate the total number of ways to arrange the selected members in a specific order.

• Permutations are used to calculate the total number of ways to select the committee without considering the order of selection, while combinations are used to calculate the total number of ways to select the committee considering the order of selection.