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? ??

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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) About Me  (Show Source):
You can put this solution on YOUR website!


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

C%2812%2C4%29=+%2812%2A11%2A10%2A9%29%2F%284%2A3%2A2%2A1%29+=+495

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) %28C%283%2C2%29%2AC%289%2C1%29%29%2B%28C%283%2C3%29%2AC%289%2C0%29%29

corrected post, RIGHT: (you are choosing a total of 4 people) %28C%283%2C2%29%2AC%289%2C2%29%29%2B%28C%283%2C3%29%2AC%289%2C1%29%29

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

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

a) How many committee of 4 student can be selected?
C%2812%2C4%29=12%21%2F%28%2812-4%29%214%21%29
C%2812%2C4%29=12%21%2F%288%214%21%29
...simplify

C%2812%2C4%29=11%2A5%2A9
C%2812%2C4%29=495
b) How many of them contain at least+2 women? ?

if there are 9 men and 3+women:
The total number of possible committees can be formed without any restrict is
12C4=495
Among them, the number of committees without any women is
9C4=126
and the number of the committee with exactly+one+woman is 3%289C3%29/
Thus the number of committees with at least+two women is:
12C4-9C4-+3%289C3%29=495-126-252=117


or, exclude the case of no women, and one woman
C%2812%2C4%29-+C%283%2C1%29%2AC%289%2C3%29+-+C%283%2C0%29%2AC%289%2C4%29
=495-%283%2A84%29-%281%2A+126%29
= 495+-+252+-+126+
= 117

Answer by ikleyn(52781) About Me  (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)  C%5B12%5D%5E4 = 495.                                            ANSWER



(b)  C%5B3%5D%5E2%2AC%5B9%5D%5E2 + C%5B3%5D%5E3%2AC%5B9%5D%5E1 = 3*36 + 1*9 = 108 + 9 = 117.      ANSWER

Solved.

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

It is why I came to correct it.


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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.