SOLUTION: A set of flash cards consists of 15 red, 12 blue, 10 black and 12 yellow cards. The cards in each colour are numbered from 1 through 15. (a) How many groups of 6 cards can be sel

Question 1180849: A set of flash cards consists of 15 red, 12 blue, 10 black and 12 yellow cards. The cards in each colour are numbered from 1 through 15.
(a) How many groups of 6 cards can be selected from the entire set?
(b) How many groups of 6 can be selected from the red cards?
(c) How many groups of 24 cards can be selected from the entire set if there must be six of each colour?
Thank you in advance for any help:)
Answer by ikleyn(52778) (Show Source): You can put this solution on YOUR website!
.
A set of flash cards consists of 15 red, 12 blue, 10 black and 12 yellow cards. The cards in each colour are numbered from 1 through 15.
(a) How many groups of 6 cards can be selected from the entire set?
(b) How many groups of 6 can be selected from the red cards?
(c) How many groups of 24 cards can be selected from the entire set if there must be six of each colour?
Thank you in advance for any help:)
~~~~~~~~~~~~~~~

The total number of the cards is 15 + 12 + 10 + 12 = 49.

The fact that the cards of each color are numbered MEANS that the cards are DISTINGUISHABLE, even if their color is the same.

The order of the cards in groups DOES NOT MATTER, so all three parts of the problem are on COMBINATIONS.

    (a)  The number of different groups of 6 cards is   = 13983816.     ANSWER


    (b)   = 5005.    ANSWER



    (c)   = 5005*924*210*924 = 897361264800.     ANSWER

All questions are answered. The problem is just solved, in full.

------------------

This problem is on COMBINATIONS.

On Combinations, see introductory lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
    - Fundamental counting principle problems
    - OVERVIEW of lessons on Permutations and Combinations
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Combinatorics: Combinations and permutations".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

RELATED QUESTIONS
There are 52 color cards. 13 red, 13 blue, 13 yellow, and 13 green. Each color has cards... (answered by stanbon)

A certain deck of cards contains 2 blue cards, 2 red cards, 2 yellow cards, and 2 green... (answered by Fombitz)

A player draws one card from a special deck of 27 playing cards shown here. The deck,... (answered by solver91311)

What are the solutions: After several rounds of a card game, a deck of playing cards... (answered by edjones)

The game of Fizzbin is played with a deck of 30 cards. There are three colors (red,... (answered by stanbon)

Consider a deck of 52 cards with the following characteristics: 13 red cards, numbered 1 (answered by solver91311)

One deck of cards consists of six cards numbered 1 through 6, and a second deck consists (answered by Fombitz)

Suppose that you are drawing cards from a set of 6 cards, the colors of which are red,... (answered by Fombitz)

suppose that you are drawing cards from a set of 6 cards, the colours of which are red ,... (answered by ewatrrr)