SOLUTION: A class contains 9 men and 3 women: a)How many committee of 4 student can be selected? Ans=495 b)How many of them contain at least 2 women? ??

Question 1179571: A class contains 9 men and 3 women:
a)How many committee of 4 student can be selected? Ans=495
b)How many of them contain at least 2 women? ??
Found 3 solutions by greenestamps, MathLover1, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

a) 12 people to choose from; you are selecting 4:

b) Here you have to choose EITHER 2 of the 3 women AND 1 of the 9 men OR all 3 of the 3 women AND 0 of the 9 men. Convert the "AND"s to multiplication and the "OR"s to addition:

(revised answer to correct some wrong numbers....)

original post, WRONG: (you are not choosing a total of 3 people)

corrected post, RIGHT: (you are choosing a total of 4 people)

You can do the calculations, similar to the one shown for part a.

Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

a) How many committee of student can be selected?

...simplify

b) How many of them contain at women? ?

if there are men and women:
The total number of possible committees can be formed without any restrict is

Among them, the number of committees any women is

and the number of the committee with woman is /
Thus the number of committees with women is:

or, exclude the case of women, and woman

=
=
=

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
A class contains 9 men and 3 women:
(a) How many committee of 4 student can be selected? Ans=495
(b) How many of them contain at least 2 women?
~~~~~~~~~~~~~~~

(a) = 495. ANSWER (b) + = 3*36 + 1*9 = 108 + 9 = 117. ANSWER

Solved.

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

In the post by @greenestamps, the formula for part (b) has an error.

It is why I came to correct it.

/////////////

This problem is on COMBINATIONS.

It combines your knowledge on combinations and the Fundamental counting principle.

To learn the subject, see these 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.

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