What are some practice problems for combinations and permutations?

What are some practice problems for combinations and permutations?

Sure! Here are a few practice problems:

1. How many ways can you arrange the letters in the word 'MATH'?
2. In how many ways can you choose 3 fruits from a basket of 5 different fruits?
3. If a committee of 4 is to be formed from 10 people, how many different committees can be formed?

Can you explain the difference between combinations and permutations?

Absolutely! Combinations are selections where the order does not matter, while permutations are arrangements where the order does matter. For example, choosing 2 fruits from a set of 5 is a combination, but arranging those 2 fruits is a permutation.

Can you give me the solutions to the problems you mentioned?

Of course! Here are the solutions:

1. The arrangements of 'MATH' = 4! = 24 ways.
2. Choosing 3 fruits from 5 = 5C3 = 10 ways.
3. Forming a committee of 4 from 10 = 10C4 = 210 ways.

What formulas should I use for combinations and permutations?

For combinations, use the formula: C(n, r) = n! / (r!(n-r)!). For permutations, use: P(n, r) = n! / (n-r)!. Here, n is the total number of items, and r is the number of items to choose.