Chapter 12: Q 11. (page 836)

Evaluate $(\begin{matrix} 1000 \\ 1000 \end{matrix})$

Short Answer

Expert verified

The value of $(\begin{matrix} 1000 \\ 1000 \end{matrix}) = 1$

Step by step solution

Step 1. Defination

if $j$ and $n$ are the integers with $0 \leq j \leq n$ , the symbol $(\begin{matrix} n \\ j \end{matrix})$ is defined as $(\begin{matrix} n \\ j \end{matrix}) = \frac{n!}{j! (n - j)!}$

Step 2. Explanation

$\Rightarrow (\begin{matrix} 1000 \\ 1000 \end{matrix}) = \frac{1000!}{1000! (1000 - 1000)!}$

localid="1647003553206" $\Rightarrow (\begin{matrix} 1000 \\ 1000 \end{matrix}) = \frac{1000 \times 999 \times 998 \dots \dots \times 1}{(1000 \times 999 \times 998 \dots \dots \times 1) (0!)}$

localid="1647003564838" $\Rightarrow (\begin{matrix} 1000 \\ 1000 \end{matrix}) = 1$

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Evaluate $(\begin{matrix} 1000 \\ 1000 \end{matrix})$

Short Answer

Step by step solution

Step 1. Defination

Step 2. Explanation

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Short Answer

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Evaluate $(\begin{matrix} 1000 \\ 1000 \end{matrix})$