Computers and Technology, 09.10.2019 21:00 Sk8terkaylee

Aperson gets 13 cards of a deck. let us call for simplicity the types of cards by 1,2,3,4. in how many ways can we choose 13 cards, so that so that there are 5 of type 1, there are 4 of type 2, there are 2 of type 3 and there are 2 of type 4?

Answers: 2

Show answers

Answers

There are 5,598,527,220 ways to choose 5 cards of type 1, 4 cards of type 2, 2 cards of type 3 and 2 cards of type 4 from a set of 13 cards.

Explanation:

The crucial point of this problem is to understand the possible ways of choosing any type of card from the 13-card deck.

This is a problem of combination since the order of choosing them does not matter here, that is, the important fact is the number of cards of type 1, 2, 3 or 4 we can get, no matter the order that they appear after choosing them.

So, the question for each type of card that we need to answer here is, how many ways are there of choosing 5 cards of type 1, 4 cards of type 2, 2 cards of type 3 and 2 are of type 4 from the deck of 13 cards?

The mathematical formula for combinations is $\\ \frac{n!}{(n-k)!k!}$ , where n is the total of elements available and k is the size of a selection of k elements from which we can choose from the total n.

Then,

Choosing 5 cards of type 1 from a 13-card deck:

$\frac{n!}{(n-k)!k!} = \frac{13!}{(13-5)!5!} = \frac{13*12*11*10*9*8!}{8!*5!} = \frac{13*12*11*10*9}{5*4*3*2*1} = 1,287$ , since $\\ \frac{8!}{8!} = 1$ .

Choosing 4 cards of type 2 from a 13-card deck:

$\\ \frac{n!}{(n-k)!k!} = \frac{13!}{(13-4)!4!} = \frac{13*12*11*10*9!}{9!4!} = \frac{13*12*11*10}{4!}= 715$ , since $\\ \frac{9!}{9!} = 1$ .

Choosing 2 cards of type 3 from a 13-card deck:

$\\ \frac{n!}{(n-k)!k!} =\frac{13!}{(13-2)!2!} = \frac{13*12*11!}{11!2!} = \frac{13*12}{2!} = 78$ , since $\\ \frac{11!}{11!}=1$ .

Choosing 2 cards of type 4 from a 13-card deck:

It is the same answer of the previous result, since

$\\ \frac{n!}{(n-k)!k!} = \frac{13!}{(13-2)!2!} = 78$ .

We still need to make use of the Multiplication Principle to get the final result, that is, the ways of having 5 cards of type 1, 4 cards of type 2, 2 cards of type 3 and 2 cards of type 4 is the multiplication of each case already obtained.

So, the answer about how many ways can we choose 13 cards so that there are 5 of type 1, there are 4 of type 2, there are 2 of type 3 and there are 2 of type 4 is:

1287 * 715 * 78 * 78 = 5,598,527,220 ways of doing that (or almost 6 thousand million ways).

In other words, there are 1287 ways of choosing 5 cards of type 1 from a set of 13 cards, 715 ways of choosing 4 cards of type 2 from a set of 13 cards and 78 ways of choosing 2 cards of type 3 and 2 cards of type 4, respectively, but having all these events at once is the multiplication of all them.

Answer from: Quest

answeroperating system;

Answer from: Quest

Key terms- a word that serves as the meaning of another wordi hope this !

Other questions on the subject: Computers and Technology

Computers and Technology, 23.06.2019 07:50, kmart4062

Apython programming question: assume s is a string of lower case characters. write a program that prints the number of times the string 'bob' occurs in s. for example, if s = 'azcbobobegghakl', then your program should print number of times bob occurs is: 2

Answers: 3

continue

Computers and Technology, 23.06.2019 09:30, caromaybelline71

Write an essay on online collaboration, how to do it, the challenges, resolving the challenges, and consider whether the risks are greater than rewards. ( need )

Answers: 1

continue

Computers and Technology, 23.06.2019 22:50, atifgujar

An environmental protection agency study of 12 automobiles revealed a correlation of 0.47 between engine size and emissions. at 0.01 significance level, can we conclude that there is a positive association between the variables? what is the p value? interpret.

Answers: 2

continue

Computers and Technology, 24.06.2019 06:30, hannahgracew12

Some peer-to-peer networks have a server and some don't. true false

Answers: 2

continue

You know the right answer?

Aperson gets 13 cards of a deck. let us call for simplicity the types of cards by 1,2,3,4. in how ma...