How many ways can 4 identical footballs and 3 identical basketballs be ordered on a shelf?

Mathematics

1 answer:

lina2011 [118]3 years ago

3 0

Answer: There are 35 ways to arrange on a shelf.

Step-by-step explanation:

Since we have given that

Number of identical footballs = 4

Number of identical basketballs = 3

We need to find the number of ways that the above can be ordered on a shelf.

Total number of books = 4+3 = 7

So, it becomes,

$=\frac{7!}{4!\times 3!}\\\\=\frac{5040}{144}\\\\=35$

Since there are 4 identical footballs i.e. 4! and 3 identical basketballs i.e. 3!. so, we divide the identical part with the whole part.

Hence, there are 35 ways to arrange on a shelf.

You might be interested in

5(w - 1 1/10) = - (w - 8 2/5)

aliina [53]

Answer:

w=3.65

Step-by-step explanation:

6 0

3 years ago

1. Taking your eyes off the road for ____ seconds at 60 miles per hour means you have traveled blindly for half the length of a

MrRa [10]

Answer:

4.09 seconds

Step-by-step explanation:

simplify miles per hour to feet per second how many feet is a mile and how many seconds are in an hour you end up with 88 fps from 60 mph

now simply a football field is 360 feet so 360/88 is 4.09090909 etc

4 0

2 years ago

The savings account offering which of these APRs and compounding periods offers the best APY?

ANTONII [103]

A)

$\bf \qquad \qquad \textit{Annual Yield Formula}
\\\\
\left. \qquad \qquad\right. \left(1+\frac{r}{n}\right)^{n}-1
\\\\
\begin{cases}
r=rate\to 3.1196\%\to \frac{3.1196}{100}\to &0.031196\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{semi-annually, thus twice}
\end{array}\to &2
\end{cases}
\\\\\\
\left. \qquad \qquad\right. \left(1+\frac{0.031196}{2}\right)^{2}-1$

b)

$\bf \qquad \qquad \textit{Annual Yield Formula}
\\\\
\left. \qquad \qquad\right. \left(1+\frac{r}{n}\right)^{n}-1
\\\\
\begin{cases}
r=rate\to 3.1184\%\to \frac{3.1184}{100}\to &0.031184\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{quarterly, thus four times}
\end{array}\to &4
\end{cases}
\\\\\\
\left. \qquad \qquad\right. \left(1+\frac{0.031184}{4}\right)^{4}-1$

c)

$\bf \qquad \qquad \textit{Annual Yield Formula}
\\\\
\left. \qquad \qquad\right. \left(1+\frac{r}{n}\right)^{n}-1
\\\\
\begin{cases}
r=rate\to 3.1095\%\to \frac{3.1095}{100}\to &0.031095\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{daily, assuming 365 days}
\end{array}\to &365
\end{cases}
\\\\\\
\left. \qquad \qquad\right. \left(1+\frac{0.031095}{365}\right)^{365}-1$

d)

$\bf \qquad \qquad \textit{Annual Yield Formula}
\\\\
\left. \qquad \qquad\right. \left(1+\frac{r}{n}\right)^{n}-1
\\\\
\begin{cases}
r=rate\to 3.1172\%\to \frac{3.1172}{100}\to &0.031172\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{monthly, thus twelve times}
\end{array}\to &12
\end{cases}
\\\\\\
\left. \qquad \qquad\right. \left(1+\frac{0.031172}{12}\right)^{12}-1$

8 0

4 years ago

Read 2 more answers

Lake County’s smallest forest preserve is 472 acres. Orange County’s smallest preserve is 482 acres. Find the ratio of the acrea

photoshop1234 [79]

Answer:

Ratio is 236 : 241

Step-by-step explanation:

Lake County’s smallest forest preserve is 472 acres. Orange County’s smallest preserve is 482 acres

Lake County’s smallest forest = 472

Orange County’s smallest = 482

To find ratio we make a fraction