Question

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

Answer 1

Answers:

Row 0:                       1

Row 1:                      1     1

Row 2:                   1    2    1

Row 3:                 1    3    3     1

Row 4:               1   4   6     4     1

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Explanation:

This is known as Pascal's Triangle. Each value, other than the '1's, is found by adding the values directly above it. For instance, the '4' is the result of 1+3, and the 6 is a result of 3+3, and so on.

You can use the nCr combination formula to find the same values.

Alternatively you can expand out binomials of the form (x+y)^n, for integer values of n, and you'll find the coefficients of the terms match perfectly with Pascal's Triangle.