What is the 6th sicth entry in row 5 of pascle's triangle?

Answer

To find the 6th entry in row 5 of Pascal's triangle, we can follow these steps:

### Step 1: Understand the structure of Pascal's Triangle
Pascal's triangle is constructed such that each entry is the sum of the two entries directly above it. The rows are indexed starting from 0. Therefore, row 0 has 1 entry, row 1 has 2 entries, row 2 has 3 entries, and so on.

### Step 2: Identify the row and entry
In this case, we need to find the 6th entry in row 5. Remember that the entries are indexed starting from 0, so:
- Row 5 has entries indexed from 0 to 5.
- The 6th entry corresponds to index 5.

### Step 3: Write out the entries in row 5
To find the entries in row 5, we can either construct the triangle or use the binomial coefficients. The entries in row 5 are given by the binomial coefficients \( C(5, k) \) for \( k = 0, 1, 2, 3, 4, 5 \):
- \( C(5, 0) = 1 \)
- \( C(5, 1) = 5 \)
- \( C(5, 2) = 10 \)
- \( C(5, 3) = 10 \)
- \( C(5, 4) = 5 \)
- \( C(5, 5) = 1 \)

Thus, the entries in row 5 are: \( 1, 5, 10, 10, 5, 1 \).

### Step 4: Identify the 6th entry
From the list of entries in row 5, the 6th entry (index 5) is \( 1 \).

### Final Answer
The 6th entry in row 5 of Pascal's triangle is **1**.

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