https://file.aiquickdraw.com/mathbot/file/1726680372041q1f4nrwy.jpg

The problem is asking to determine how many ways to make a necklace consisting of 4 different beads chosen from 7 distinct beads, with the condition that 2 specific beads must be included and cannot be adjacent.

### Step-by-step approach:

1. **Identify total beads:**
   There are 7 distinct beads available, and we are selecting 4 beads for the necklace.

2. **Mandatory beads:**
   Two specific beads must always be included in the arrangement.

3. **No adjacency condition:**
   These two mandatory beads cannot be placed next to each other.

4. **Combinatorial approach:**
   - First, choose 2 more beads from the remaining 5 beads (since two are already mandatory).
   - Arrange the 4 beads in a circle (for the necklace), ensuring the two mandatory beads are not adjacent.

I can now calculate the solution using combinatorial formulas. Let me proceed with that.The total number of ways to create the necklace, ensuring the two mandatory beads are included and not adjacent, is **60**.

Would you like further explanation, or have any other questions? Here are five related questions you might want to explore:

1. How does the solution change if the necklace is linear instead of circular?
2. What if the condition is relaxed so that the mandatory beads can be adjacent?
3. How many ways are there to arrange all 7 beads in a circular necklace?
4. What if we allow repetition of beads in the selection process?
5. How would the solution change if we needed to choose 5 beads instead of 4?

**Tip:** When solving combinatorial problems involving restrictions like adjacency, it's often useful to think about the positions that remain after placing restricted elements.

Tentukan banyak cara membuat kalung terdiri dari 4 manik-manik berbeda yang diambil dari 7 manik-manik berbeda dengan syarat 2 manik-manik tertentu harus ada dan tidak boleh berdampingan.

Discover how to solve a combinatorial problem involving the creation of a necklace with 4 different beads selected from 7, where 2 specific beads must be included but not adjacent. Learn key concepts in combinatorics and circular permutations, suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation