Chapter 5: Q .21. (page 247)

. Determine the value of each binomial coefficient.
a. $(\begin{array}{l} 8 \\ 3 \end{array})$
b. $(\begin{array}{l} 8 \\ 5 \end{array})$
c. $(\begin{array}{l} 6 \\ 6 \end{array})$
d. $(\begin{array}{l} 10 \\ 2 \end{array})$
e. $(\begin{matrix} 40 \\ 4 \end{matrix})$
f. $(\begin{matrix} 100 \\ 0 \end{matrix})$

Short Answer

Expert verified

Part a) $56$

Part b) $56$

Part c) $1$

Part d) $45$

Part e) $91390$

Part f) $1$

Step by step solution

Step 1:Given Information

a. $(\begin{array}{l} 8 \\ 3 \end{array})$

b. $(\begin{array}{l} 8 \\ 5 \end{array})$

c. $(\begin{array}{l} 6 \\ 6 \end{array})$

d. $(\begin{matrix} 10 \\ 2 \end{matrix})$

e. $(\begin{matrix} 40 \\ 4 \end{matrix})$

f. $(\begin{matrix} 100 \\ 0 \end{matrix})$

Step 2:Simplification Part a)

$(\begin{array}{l} 8 \\ 3 \end{array}) = \frac{8!}{3! \times (8 - 3)!}$

$= \frac{8!}{3! \times 5!}$

$= 56$

Step 2:Simplification Part b)

$(\begin{array}{l} 8 \\ 5 \end{array}) = \frac{8!}{5! \times (8 - 5)!}$

$= \frac{8!}{3! \times 5!}$

$= 56$

Step 2:Simplification Part c)

$(\begin{array}{l} 6 \\ 6 \end{array}) = \frac{6!}{6! \times (6 - 6)!}$

$= \frac{6!}{6! \times 0!}$

$= 1$

Step 2:Simplification Part d)

$(\begin{matrix} 10 \\ 2 \end{matrix}) = \frac{10!}{2! \times (10 - 2)!}$

$= \frac{6!}{2! \times 8!}$

$= 45$

Step 2:Simplification Part e)

$(\begin{matrix} 40 \\ 4 \end{matrix}) = \frac{40!}{4! \times (40 - 4)!}$

$= \frac{40!}{4! \times 36!}$

$= 91390$

Step 2:Simplification Part f)

$(\begin{matrix} 100 \\ 0 \end{matrix}) = \frac{100!}{0! \times (100 - 0)!}$

$= \frac{100!}{0! \times 100!}$

$= 1$

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Short Answer

Step by step solution

Step 1:Given Information

Step 2:Simplification Part a)

Step 2:Simplification Part b)

Step 2:Simplification Part c)

Step 2:Simplification Part d)

Step 2:Simplification Part e)

Step 2:Simplification Part f)

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. Determine the value of each binomial coefficient.a. 83b. 85c. 66d. 102e. 404f. 1000

Short Answer

Step by step solution

Step 1:Given Information

Step 2:Simplification Part a)

Step 2:Simplification Part b)

Step 2:Simplification Part c)

Step 2:Simplification Part d)

Step 2:Simplification Part e)

Step 2:Simplification Part f)

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Most popular questions from this chapter

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