Question

NEED HELP PLEASE

Complete the table to find the pattern in the number of combinations.


Row 0 0C0 = 1

Row 1 1C0 = 1 1C1 = 1

Row 2 2C0 = 1 2C1 = ? 2C2 = 1

Row 3 3C0 = 1 3C1 =? 3C2 = ? 3C3 = 1

Row 4 4C0 = 1 4C1 = ? 4C2 = ? 4C3 =? 4C4 = 1

Answer 1

9514 1404 393

Answer:

see attached

Explanation:

The formula for nCk is ...

nCk = n!/(k!(n -k)!)

It always works out that nC0 = 1 and nC1 = n, and the sequence of numbers across a row of the diagram is symmetrical about the center.

This means you only need to calculate one value to finish filling your diagram.

4C2 = 4!/(2!(2!)) = (4·3)/(2·1) = 6

You will find the pattern to be ...

each element in the diagram is the sum of the two above it.