Probability and Combinatorics Flashcard

Front

How many ways can 3 books be arranged on a shelf?

Back

6 (3! = 3 × 2 × 1 = 6)

Front

What is the probability of rolling a 2 or a 5 on a die?

Back

1/3 (There are 2 favorable outcomes out of 6 possible outcomes.)

Front

How many combinations can be made by choosing 2 fruits from 5?

Back

10 (Calculated using the combination formula C(n, k) = n! / (k!(n-k)!) where n=5 and k=2.)

Front

What is the probability of rolling a 2 and a 5, and flipping heads with two dice and a coin?

Back

1/72 (Probability of rolling a 2 and a 5 is 1/36, and flipping heads is 1/2. So, (1/36) * (1/2) = 1/72.)

Front

How many 3-letter codes can be made from the letters A, B, C, D if no letter repeats?

Back

24 (Calculated using permutations: P(n, r) = n! / (n-r)! where n=4 and r=3.)

Front

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

Back

P(n, r) = n! / (n - r)! (This formula calculates the number of ways to arrange r items from n distinct items.)

Front

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

Back

C(n, r) = n! / (r!(n - r)!) (This formula calculates the number of ways to choose r items from n distinct items without regard to the order.)

Front

If you roll a die, what is the probability of rolling an even number?

Back

1/2 (There are 3 even numbers: 2, 4, 6 out of 6 possible outcomes.)

Front

What is the total number of outcomes when flipping a coin and rolling a die?

Back

12 (2 outcomes for the coin and 6 outcomes for the die: 2 × 6 = 12.)

Front

What is the probability of drawing a red card from a standard deck of cards?

Back

1/2 (There are 26 red cards out of 52 total cards.)