(10 points) From a group of 9 men and 7 women a committee consisting of 4 men and 4 women is to be formed. How many different committees are possible if (a) 2 of the men refuse to serve together? (a) 2 of the women refuse to serve together? (a) 1 man and 1 woman refuse to serve together?

a) 2450

b) 1890

c) 1050

Step-by-step explanation:

Given:

- Available Group = 9 M & 7 F

- Committee of= 4 M and 4 W to be formed

Find:

- (a) 2 of the men refuse to serve together?

- (a) 2 of the women refuse to serve together?

- (a) 1 man and 1 woman refuse to serve together?

Solution:

- The question pertains to a selection process, We will use combinations for each case as follows.

part a)

- Since 2 men cant be selected together. Then we have to discount for one man while selecting Man for the committee. Hence, the combinations are:

                                   8C4 x 7C4 = 2450

part b)

- Since 2 women cant be selected together. Then we have to discount for one woman while selecting them for the committee. Hence, the combinations are:

                                   9C4 x 6C4 = 1890

part b)

- Since 1 women and a man cant be selected together. Then we have to discount for one woman and one man while selecting them for the committee. Hence, the combinations are:

                                   8C4 x 6C4 = 1050

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.  

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.