What is the r value in permutations?

The r value in permutations represents the number of items being selected from a larger set.

How many different license plates can be made with 6 characters (letters and numbers) without repetition?

The total number of characters is 36 (26 letters + 10 digits). The number of ways to choose 6 characters without repetition is: $$36 × 35 × 34 × 33 × 32 × 31 = 1402410240$$ .

How many ways can you choose 3 different kinds of cookies from 12 kinds?

Use the combination formula: $$C(12, 3) = \frac{12!}{3!(12-3)!} = 220$$ .

If you want to select 5 DVDs from a collection of 20, how do you calculate it?

Use the combination formula: $$C(20, 5) = \frac{20!}{5!(20-5)!}$$ .

What is the formula for calculating permutations of n items taken r at a time?

The formula is: $$P(n, r) = \frac{n!}{(n-r)!}$$ .

What is the formula for calculating combinations of n items taken r at a time?

The formula is: $$C(n, r) = \frac{n!}{r!(n-r)!}$$ .

How many ways can you choose 3 pies from 8 available pies?

Use the combination formula: $$C(8, 3) = \frac{8!}{3!(8-3)!} = 56$$ .

What does 'without repetition' mean in the context of permutations and combinations?

'Without repetition' means that once an item is selected, it cannot be selected again in that arrangement or selection.

Probability: Permutations & Combinations Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a permutation?

Back

2.

FLASHCARD QUESTION

Front

What is a combination?

Back

3.

FLASHCARD QUESTION

Front

What is the difference between permutations and combinations?

Back

Permutations consider the order of selection, while combinations do not. For example, selecting A, B, C is different in permutations (ABC, ACB, etc.) but the same in combinations (ABC).

4.

FLASHCARD QUESTION

Front

How do you calculate the number of ways to choose r items from n items?

Back

5.

FLASHCARD QUESTION

Front

What is the factorial of a number?

Back

6.

FLASHCARD QUESTION

Front

How many ways can you arrange 3 books out of 5?

Back

7.

FLASHCARD QUESTION

Front

If you have 10 different shirts, how many ways can you choose 4 shirts?

Back

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