Question

Which of the following demonstrates how the 20 is calculated using the combination pattern?

Answer 1

Answer:

D

Step-by-step explanation:

The diagram shows Pascal's triangle. Pascal's triangle is a triangular array of the binomial coefficients.

The entry in the $n^{th}$ row (start counting rows from 0) and $k^{th}$ column (start counting columns from 0) of Pascal's triangle is denoted by

$C^n_k=\left(\begin{array}{c}n\\ k\end{array}\right)$

Coefficient 20 stands in 6th row, then n = 6 and in 3rd column, so k = 3.

Hence,

$20=C^6_3=\left(\begin{array}{c}6\\ 3\end{array}\right)=\dfrac{6!}{3!(6-3)!}$