Question 1106310: Hi, Im having a trouble regarding permutations and combinations when the questions are like this:
1. Grade 10 class wants to send two representatives to participate in the school singing contest. Six boys and eight girls are willing to be representatives. In how many was can the two representatives be chosen if
a. there is at least 1 girl?
b. the two representative are of the same sex?
2. A committee of 5 members is formed from 6 men and 7 women. Find the number of ways to form the committee in each of the following cases.
a. there are exactly 3 women
b. there are more men than women
c. there are at least 4
3. How many ways can the numbers 2 – 10 be arranged in a row if any two of the prime numbers are not placed next to each other?
4. Seven marbles are chosen from 10 marbles of different colors. They are lined up into two lines in which the first line has 2 marbles and the second line has 5 marbles.
a. In how many ways can this be done?
b. If the red and blue marbles must be in the first line, how many possible arrangements are there?
Please help me understand this lesson. I'll be having our test tomorrow. I want to pass! I'm not reall good at word problems 😫😫 Thank you in advance! ☺️
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 1. Total number of possibilities. are 14C2=14*13/2 = 91
How many ways are there with NO girls? Start with 6C2, both boys, and that is 15 ways. The other 76 ways would have at least 1 girl.
MM have 15 ways. FF is 8C2=28 ways, so there are 43 ways.
----------------
2. exactly 3 women would be 2 men, so it is 7C3*6C2=35*15=525 ways.
more men than women would require 5-0, 4-1, 3-2, so the number of ways for the first is 6C5=6 PLUS
6C4*7C1=15*7=105 ways PLUS 6C3*7C2=20*21=420 ways. Total is 531 ways
Not clear at least 4. If men, 6C4*7C1=105+6C5*7C0=6=111 ways
If at least 4 women, 6C1*7C4=6*35=210 ways plus 6C0*7C5=21 ways or 231 ways
1287 total ways (13C5).
Rest can be resubmitted.
Answer by ikleyn(52754)  (Show Source):
|
|
|
