Question 1174742: How many ways are there of filling 5 different job vacancies between 7 ladies, given that each woman can only do just one job
Found 2 solutions by ewatrrr, ikleyn:
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi
How many ways are there of filling 5 different job vacancies between 7 ladies,
given that each woman can only do just one job
7C5 = 21 ways
Use Your calculator or nCr = (n!)/(r!(n - r)!).
This done with a Casio fx-115 ES (cost< $20)
Wish You the Best in your Studies.
Answer by ikleyn(52777)  (Show Source):
You can put this solution on YOUR website! .
Jobs are different and women are different,
T H E R E F O R E
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| in this problem the order of arranging DOES MATTER. |
+-------------------------------------------------------+
THEREFORE, the answer is 7*6*5*4*3 = 2520 ways.
It is the product of 5 consecutive integer numbers in descending order starting from 7.
First job vacancy can be filled by any of 7 ladies, giving 7 options.
Second job vacancy can be filled by any of remaining 6 ladies, giving 6 options
. . . and so on to the last, 5-th vacancy inclusive.
It gives the formula.
All these arrangements are DIFFERENT.
Solved, answered and explained. And completed.
Do not accept any other answer.
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How @ewatrrr interprets, solves and answers this problem, is INCORRECT.
Since the order is IMPORTANT, this problem is on PERMUTATIONS.
It is NOT on COMBINATIONS.
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It is the MAJOR POINT in the solution of this problem
to recognize to which type it does really belong.
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@ewatrrr teaches you INCORRECTLY in this major point.
She does it incorrectly EVERY DAY, because she DOES NOT know the subject.
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To see many other similar solved problems, look into the lesson
- Special type permutations problems
in this site.
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