Problem

Read the combination value directly from Pascal's triangle. ${ }_{6} \mathrm{C}_{2}$ \[ { }_{6} C_{2}=\square \]

Solution

Step 1 :Refer to Pascal's triangle, which is a triangular array of the binomial coefficients. Each number is the sum of the two directly above it. The rows and columns of Pascal's triangle start from 0.

Step 2 :Here is how the first few rows of Pascal's triangle look like: \[\begin{array}{c} 0: & 1 \\ 1: & 1 & 1 \\ 2: & 1 & 2 & 1 \\ 3: & 1 & 3 & 3 & 1 \\ 4: & 1 & 4 & 6 & 4 & 1 \\ 5: & 1 & 5 & 10 & 10 & 5 & 1 \\ 6: & 1 & 6 & 15 & 20 & 15 & 6 & 1 \end{array}\]

Step 3 :The combination value ${ }_{6} C_{2}$ refers to the 2nd element in the 6th row of Pascal's triangle (remember we start counting from 0).

Step 4 :Looking at the 6th row of Pascal's triangle, we can see that the 2nd element is 15.

Step 5 :So, ${ }_{6} C_{2} = 15$.

Step 6 :Therefore, the final answer is \(\boxed{15}\).

From Solvely APP
Source: https://solvelyapp.com/problems/jKwVfXIXLg/

Get free Solvely APP to solve your own problems!

solvely Solvely
Download