Math Problem Statement

Suppose we want to choose colors, without replacement, from the colors red, blue, green, purple, and yellow.

Solution

To choose kk colors without replacement from the 5 available colors (red, blue, green, purple, yellow), we can use combinations, as the order of selection does not matter. The number of ways to choose kk colors from 5 can be calculated using the combination formula:

(nk)=n!k!(nk)!\binom{n}{k} = \frac{n!}{k!(n-k)!}

where nn is the total number of colors (5 in this case) and kk is the number of colors chosen.

Would you like to know how to calculate this for specific values of kk?

Here are some related questions to consider:

  1. How many combinations are there for choosing 2 colors?
  2. What if we wanted to choose all 5 colors?
  3. How does the combination formula change if we choose colors with replacement?
  4. Can you explain how to calculate (53)\binom{5}{3}?
  5. What is the significance of combinations in real-world scenarios?

Tip: Remember that when choosing without replacement, each selection reduces the number of available options.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Combinations
Probability

Formulas

Combination formula \( \binom{n}{k} = \frac{n!}{k!(n-k)!} \)

Theorems

Combination theorem

Suitable Grade Level

Grades 7-9