Chapter 12: Q 13. (page 836)

Evaluate $(\begin{matrix} 55 \\ 23 \end{matrix})$

Short Answer

Expert verified

The value of $(\begin{matrix} 55 \\ 23 \end{matrix}) = 1866442158555973$

Step by step solution

Step 1. Defination

if $j$ and $n$ are integer with $o \leq j \leq n$ , 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

$\Rightarrow (\begin{matrix} 55 \\ 23 \end{matrix}) = \frac{55!}{23! (55 - 23)!}$

$\Rightarrow (\begin{matrix} 55 \\ 23 \end{matrix}) = \frac{55 \times 54 \times 53 \times 52 \dots \dots \times 1}{(23 \times 22 \times 21 \dots \dots \times 1) (32 \times 31 \times 30 \dots \dots \times 1)}$

$\Rightarrow (\begin{matrix} 55 \\ 23 \end{matrix}) = 1866442158555973$

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Evaluate $(\begin{matrix} 55 \\ 23 \end{matrix})$

Short Answer

Step by step solution

Step 1. Defination

Step 2. Explanation

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Evaluate5523

Short Answer

Step by step solution

Step 1. Defination

Step 2. Explanation

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Evaluate $(\begin{matrix} 55 \\ 23 \end{matrix})$