in how many ways can you select 5 red cards and 2 black cards from 10 red cards ...

Questions

nicaela99 @nicaela99

September 2022 1 1 Report

in how many ways can you select 5 red cards and 2 black cards from 10 red cards and 9 black cards?

Answers & Comments

TheoD

Verified answer

$\mathbb{SOLUTION:}$

According to the problem there are :

5 cards selected from 10 cards
2 cards selected from 9 cards

Using the formula of Combination,

$\quad\quad\quad\begin{gathered}\boxed{\rm{C} = \frac{n!}{r!(n - r)!}} \end{gathered}$

Let's find the ways

5 red cards are selected from 10 red cards :

$\begin{gathered} \rm{C} = \frac{\rm n!}{\rm r!(n - r)!} \end{gathered}$

$\begin{gathered} \rm{C} = \frac{10!}{5!(10 - 5)!} \end{gathered}$

$\begin{gathered} \rm{C} = \frac{10!}{5!\ 5!} \end{gathered}$

$\begin{gathered} \rm{C} = \frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot \bcancel{5}}{\bcancel{5!}\ 5!} \end{gathered}$

$\begin{gathered} \rm{C} = \frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6}{5 \cdot 4 \cdot 4 \cdot 2 \cdot 1} \end{gathered}$

$\begin{gathered} \rm{C} = \frac{30240}{120} \end{gathered}$

$\begin{gathered} \rm{C} = 252 \end{gathered}$

2 black cards selected from 9 black cards :

$\begin{gathered} \rm{C} = \frac{\rm n!}{\rm r!(n - r)!} \end{gathered}$

$\begin{gathered} \rm{C} = \frac{9!}{2!(9 - 2)!} \end{gathered}$

$\begin{gathered} \rm{C} = \frac{9!}{7!\ 2!} \end{gathered}$

$\begin{gathered} \rm{C} = \frac{9 \cdot 8 \cdot \bcancel{7}}{\bcancel{7!}\ 2!} \end{gathered}$

$\begin{gathered} \rm{C} = \frac{9 \cdot 8}{2 \cdot 1} \end{gathered}$

$\begin{gathered} \rm{C} = \frac{72}{2} \end{gathered}$

$\begin{gathered} \rm{C} = 36 \end{gathered}$

Therefore, 5 red cards are selected from 10 red cards are have a total of 252 ways, and 2 black cards selected from 9 black cards have a 36 ways. To find the final answer, we need to multiply.

$\begin{gathered} \rm{C} = 252 \cdot 36 \end{gathered}$

$\begin{gathered} \rm{C} = 9072 \end{gathered}$

Hence, 9072 ways can be selected

Answer : $\boxed{\rm 9072 \: ways}$

arunadelvalle hello po pwede po pahelp po sa mga question ko po sa math po thank you po sorry po sa abala

arunadelvalle Hi, magandang hapon! Maaari mo ba akong tulungan sa aking tanong sa Math? Paumanhin sa abala.

Narito ang link sa aking tanong:

Note: Please answer my question correctly, nonsense answer will be reported.
https://brainly.ph/question/26369429?utm_source=android&utm_medium=share&utm_campaign=question

Note: Please answer my question correctly, nonsense answer will be reported.

neilmarisidro2520 Hi, magandang gabi! Maaari mo ba akong tulungan sa aking tanong sa Math? Paumanhin sa abala.

Narito ang link sa aking tanong:

hi! ace, genius and moderators! kindly help me in my Math? please don't waste my points, answer it correctly! thanks! sa...
https://brainly.ph/question/26402870?utm_source=android&utm_medium=share&utm_campaign=question

Note: Please answer my question correctly, nonsense answer will be reported.

neilmarisidro2520 Hi, magandang umaga! Maaari mo ba akong tulungan sa aking tanong sa Math? Paumanhin sa abala.

Narito ang link sa aking tanong:

hi! ace, genius and moderators! kindly help me in my Math? please don't waste my points, answer it correctly! thanks! sa...
https://brainly.ph/question/26402870?utm_source=android&utm_medium=share&utm_campaign=question

Note: Please answer my question correctly, nonsense answer will be reported.