.
An office consists of seven men and four women. If three are chosen for a committee,
how many of these committees will contain exactly one woman.
Please help me understand the process of solving this question;
is the multiplicative principle used or is the additive principle used?
~~~~~~~~~~~~~~~~
There is one woman and 2 men in the committee.
You can select one woman from 4 women in 4 different ways (4 = , using the combination language).
You can select two men from 7 men in = = 7*3 = 21 different ways.
You combine the committee of 3 (1 woman and 2 men) in 4*21 different ways.
This logical chain completes the solution.
Solved.
----------------
The multiplicative principle is used.
More precisely, the fundamental counting principle is used;
but you should accurately prepare the input combinations for this principle.
///////////////
On Combinations, see the lessons
- Introduction to Combinations
- PROOF of the formula on the number of Combinations
- Problems on Combinations
- Problems on Combinations with restrictions
- Fundamental counting principle problems
- Some twisted combinatorics problem
- Math circle level problem on Combinations
- 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.