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Chapter 12: Q 8. (page 836)

Evaluate $(\begin{matrix} 9 \\ 7 \end{matrix})$

Short Answer

Expert verified

The value of $(\begin{matrix} 9 \\ 7 \end{matrix}) = 36$ $(\begin{matrix} 9 \\ 7 \end{matrix}) = 36$ $(\begin{matrix} 9 \\ 7 \end{matrix}) = 36$

Step by step solution

01

Step 1. Defination

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

02

Step 2. Explanation

$\Rightarrow (\begin{matrix} 9 \\ 7 \end{matrix}) = \frac{9!}{7! (9 - 7)!}$

$\Rightarrow (\begin{matrix} 9 \\ 7 \end{matrix}) = \frac{9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{(7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1) (2 \times 1)}$

$\Rightarrow (\begin{matrix} 9 \\ 7 \end{matrix}) = 36$

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Most popular questions from this chapter

Education IRA: On January 1, 1999, John’s parents decided to place \(45 at the end of each month into an Education IRA.

(a) Find a recursive formula that represents the balance at the end of each month if the rate of return is assumed to be 6% per annum compounded monthly.

(b) How long will it be before the value of the account exceeds \)4000?

(c) What will be the value of the account in 16 years when John goes to college?

In Problems 37–50, a sequence is defined recursively. Write down the first five terms.

$a_{1} = - 2; a_{n} = n + a_{n - 1}$

A(n) _______ is a function whose domain is the set of positive integers.

In Problems 11–16, evaluate each factorial expression.

$\frac{3! 7!}{4!}$

In Problems 11–16, evaluate each factorial expression.

$\frac{9!}{6!}$

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