Probability Flashcard

Front

What is the fundamental principle of counting in probability?

Back

The fundamental principle of counting states that if one event can occur in 'm' ways and a second event can occur independently in 'n' ways, then the two events can occur in m × n ways.

Front

How do you calculate the total number of combinations when choosing 'r' items from 'n' items?

Back

The total number of combinations is calculated using the formula C(n, r) = n! / (r!(n - r)!), where '!' denotes factorial.

Front

What is a permutation?

Back

A permutation is an arrangement of objects in a specific order. The number of permutations of 'n' objects taken 'r' at a time is given by P(n, r) = n! / (n - r)!.

Front

What is the difference between combinations and permutations?

Back

Combinations are selections where the order does not matter, while permutations are arrangements where the order does matter.

Front

If you have 7 types of bread, 12 spreads, and 3 toppings, how do you find the total combinations of toast?

Back

Multiply the number of options: 7 (breads) × 12 (spreads) × 3 (toppings) = 252 different types of toast.

Front

How many different 4-digit PINs can be created if digits cannot be repeated?

Back

The number of different 4-digit PINs is calculated as 10 × 9 × 8 × 7 = 5,040.

Front

What is the formula for calculating the number of ways to choose 'r' items from 'n' items without regard to order?

Back

The formula is C(n, r) = n! / (r!(n - r)!).

Front

How many different sundaes can be made with 3 ice cream flavors, 4 toppings, and 2 sauces?

Back

Multiply the options: 3 (ice creams) × 4 (toppings) × 2 (sauces) = 24 different sundaes.

Front

What is the total number of ways to choose 5 candy bars from 14?

Back

The number of ways is calculated using combinations: C(14, 5) = 2002.

Front

What does 'n!' represent in probability and combinatorics?

Back

'n!' (n factorial) represents the product of all positive integers up to 'n'. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.