Permutations

Front

What is a permutation?

Back

A permutation is an arrangement of objects in a specific order. The order of arrangement is important.

Front

How do you calculate the number of permutations of n objects taken r at a time?

Back

The formula is P(n, r) = n! / (n - r)!, where n is the total number of objects and r is the number of objects to arrange.

Front

What is the factorial of a number?

Back

The factorial of a number n (denoted as n!) is the product of all positive integers up to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.

Front

How many ways can a club select a president, vice president, and a secretary from a group of 5 people?

Back

60 ways (calculated as P(5, 3) = 5! / (5 - 3)! = 5 × 4 × 3 = 60).

Front

What is the number of possible outcomes when a coin is tossed 6 times?

Back

64 outcomes (calculated as 2^6 = 64, since each toss has 2 possible outcomes: heads or tails).

Front

How many different codes can be formed with one digit (excluding 0) followed by one letter (excluding O)?

Back

225 codes (9 choices for digits 1-9 and 26 letters - 1 letter O = 9 × 25 = 225).

Front

A restaurant offers four appetizers, nine entrees, and three desserts. How many different ways can a three-course meal be chosen?

Back

108 ways (calculated as 4 × 9 × 3 = 108).

Front

How many ways can a disc jockey choose and arrange three songs from nine available songs?

Back

504 ways (calculated as P(9, 3) = 9! / (9 - 3)! = 9 × 8 × 7 = 504).

Front

What is the difference between permutations and combinations?

Back

Permutations consider the order of arrangement, while combinations do not. For example, choosing 3 out of 5 objects is different in permutations (order matters) than in combinations (order does not matter).

Front

What is the formula for combinations?

Back

The formula for combinations is C(n, r) = n! / [r!(n - r)!], where n is the total number of objects and r is the number of objects to choose.