Dean Chalmers and Julian Gilbey Solutions for Chapter: Permutations and Combinations, Exercise 3: EXERCISE 5A

Use your calculator to find the smallest value of $n$ for which:

$\left(n!\right)!>{10}^{20}$

Use your calculator to find the largest value of $n$ for which:

$\frac{n!}{500000}<80$

Use your calculator to find the largest value of $n$ for which:

$1.5\times {10}^{12}-n!>0$

Use your calculator to find the largest value of $n$ for which:

$\frac{n!}{(n-2)!}<500$

Express, in as many different ways as possible, the numbers $144, 252$ and $1\frac{1}{2}$ in the form $\frac{a!\times b!}{c!},$ where none of $a, b$ or $c$ is equal to $0$ or to $1.$

Express the area of a $53 \mathrm{cm}$ by $52 \mathrm{cm}$ rectangle using factorials.

Two cubical boxes measure $25 \mathrm{cm}$ by $24 \mathrm{cm}$ by $23 \mathrm{cm},$ and $8 \mathrm{cm}$ by $7 \mathrm{cm}$ by $6 \mathrm{cm}.$ Express the difference between their volumes using factorials.

Eight children each have seven boxes of six eggs and each egg is worth $\$0.09.$ Write the total value of all these eggs in dollars, using factorials.