Mathematics, 24.06.2021 22:00 Lydiac8715

(b). A club consists of 6 freshmen, 5 sophomores, and 4 juniors. How many committees of four people not from one class

Answers: 3

Show answers

Answers

Answer from: carolynhstevens

1344 committees can be formed of four people not from one class

Step-by-step explanation:

We are given:

Members in freshmen = 6

Members in sophomores = 6

Members in juniors = 6

To form a committee of four people not from one class, numerous combinations can occur. They are:

When in a committee, at least one of them are from each class

When 2 from freshmen, 1 from sophomores, and 1 from junior. The possibility becomes $^6C_2\times ^5C_1\times ^4C_1$

When 1 from freshmen, 2 from sophomores, and 1 from junior. The possibility becomes $^6C_1\times ^5C_2\times ^4C_1$

When 1 from freshmen, 1 from sophomores, and 2 from junior. The possibility becomes $^6C_1\times ^5C_1\times ^4C_2$

Total combinations: $(^6C_2\times ^5C_1\times ^4C_1)+(^6C_1\times ^5C_2\times ^4C_1)+(^6C_1\times ^5C_1\times ^4C_2)=(300+240+180)=720$

If two members come from same class

When 2 from freshmen, 2 from sophomores, and 0 from junior. The possibility becomes $^6C_2\times ^5C_2\times ^4C_0$

When 0 from freshmen, 2 from sophomores, and 2 from junior. The possibility becomes $^6C_0\times ^5C_2\times ^4C_2$

When 2 from freshmen, 0 from sophomores, and 2 from junior. The possibility becomes $^6C_2\times ^5C_0\times ^4C_2$

Total combinations: $(^6C_2\times ^5C_2\times ^4C_0)+(^6C_0\times ^5C_2\times ^4C_2)+(^6C_2\times ^5C_0\times ^4C_2)=(150+60+90)=300$

If three members come from same class

When 3 from freshmen, 1 from sophomores, and 0 from junior. The possibility becomes $^6C_3\times ^5C_1\times ^4C_0$

When 3 from freshmen, 0 from sophomores, and 1 from junior. The possibility becomes $^6C_3\times ^5C_0\times ^4C_1$

When 0 from freshmen, 3 from sophomores, and 1 from junior. The possibility becomes $^6C_0\times ^5C_3\times ^4C_1$

When 1 from freshmen, 3 from sophomores, and 0 from junior. The possibility becomes $^6C_1\times ^5C_3\times ^4C_0$

When 0 from freshmen, 1 from sophomores, and 3 from junior. The possibility becomes $^6C_0\times ^5C_1\times ^4C_3$

When 1 from freshmen, 0 from sophomores, and 3 from junior. The possibility becomes $^6C_1\times ^5C_0\times ^4C_3$

Total combinations: $[(^6C_3\times ^5C_1\times ^4C_0)+(^6C_3\times ^5C_0\times ^4C_1)+(^6C_0\times ^5C_3\times ^4C_1)+(^6C_1\times ^5C_3\times ^4C_0)+(^6C_0\times ^5C_1\times ^4C_3)+(^6C_1\times ^5C_0\times ^4C_3)]=(100+80+40+60+20+24)=324$

Total number of committees that can be formed = [720 + 300 + 324] = 1344

Hence, 1344 committees can be formed of four people not from one class

Answer from: Quest

5x+2x=49

7x=49

x=7. 35 apples

Answer from: Quest

answer: the two figures are congruent.

step-by-step explanation: they're congruent because figure efgh is reflected across the x and y axis but it was also rotated.

hope it !

(02.05 mc) determine if the two figures are congruent and explain your answer.

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 18:30, FailingstudentXD

Do some research and find a city that has experienced population growth. determine its population on january 1st of a certain year. write an exponential function to represent the city’s population, y, based on the number of years that pass, x after a period of exponential growth. describe the variables and numbers that you used in your equation.

Answers: 3

continue

Mathematics, 22.06.2019 00:30, atran6955

The graph of f(x) is obtained by reflecting the graph of f(x)=-3|x| over the x-axis. which equation describes f(x)? a) f(x)=3|x| b) f(x)=|x+3| c) f(x)=-3|x| d) f(x) = - |x+3|

Answers: 1

continue

Mathematics, 22.06.2019 00:50, Pmedellin27

Acube has a volume of 800 cubic inches. whatis the length of an edge of the cube, in inches? a. 23/100b. 43/50c. 83/100d. 1003/2e. 1003/8

Answers: 2

continue

Mathematics, 22.06.2019 01:00, zuleromanos

If log_3(x)=4.5 and log_3(y)=3, what is log_3(x^2/y)? a. 3b. 6.75c. 6d. 1.5

Answers: 2

continue

You know the right answer?

(b). A club consists of 6 freshmen, 5 sophomores, and 4 juniors. How many committees of four people...