Combinatorics and Permutations Problems

Front

What is the probability of selecting one brown cow and one white cow from a farm with 5 brown cows and 10 white cows when 2 cows escape?

Back

The probability is 5/21.

Front

What does 6P5 represent in combinatorics?

Back

6P5 represents the number of permutations of 6 items taken 5 at a time, which equals 720.

Front

How do you calculate the probability of not selecting a lime from a box containing 3 limes, 5 grapes, and 2 oranges?

Back

P(NOT lime) = (Total fruits - Limes) / Total fruits = 7/10.

Front

How many possible lock codes can be created with 4 dials, each having digits from 0 to 9?

Back

There are 10,000 possible lock codes.

Front

How many different selections of 3 flavors can be made from 15 different ice cream flavors?

Back

There are 455 different selections.

Front

Define permutations in combinatorics.

Back

Permutations are arrangements of objects in a specific order.

Front

Define combinations in combinatorics.

Back

Combinations are selections of objects without regard to the order.

Front

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

Back

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

Front

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

Back

The formula is nCr = n! / [r!(n - r)!].

Front

If a box contains 10 items, how many ways can you choose 3 items?

Back

Using combinations, the number of ways is 10C3 = 120.