Probability and combinations

Front

What is a permutation?

Back

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

Front

What is a combination?

Back

A combination is a selection of objects where the order does not matter. It focuses on the group rather than the arrangement.

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

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

Back

The formula 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.

Front

What is the probability of an event?

Back

The probability of an event is the number of favorable outcomes divided by the total number of possible outcomes.

Front

If a jar contains 8 marbles (3 red, 5 blue), what is the probability of selecting a red marble?

Back

The probability is 3/8.

Front

What is the probability of selecting a red marble, replacing it, and then selecting another red marble?

Back

The probability is (3/8) * (3/8) = 9/64.

Front

In a scenario where a letter is chosen from the word 'MATH', what is the probability of choosing 'M'?

Back

The probability is 1/4, since there are 4 letters.

Front

What is the total number of ways to choose 4 siblings from 7?

Back

The total number of ways is C(7, 4) = 35.

Front

What is the probability of selecting a brown M&M from a bowl containing 20 M&Ms?

Back

The probability is 2/20 or 1/10.