There are 40 people on the faculty. Of the 40, 15 are men and 25 are women. Use

Question

There are 40 people on the faculty. Of the 40, 15 are men and 25 are women. Use this information to answer the following questions:
a) A committee of 8 is to be selected by the principal. How many possible committees can be created, regardless of gender?
b) i. all men
    ii. all women
    iii. 4 men and 4 women
    iv. at least 2 men
     v. no more than 3 men
    iv. 5 women and 3 men
c) The principal now has his 8 members. Answer the following questions about these 8. Assume only 8 chairs for them to sit.
   i. if they sit at large table (in a line), jow many ways can they be seated?
   ii. how many ways can they be seated in a circle?
iii. if they are in a line, how many ways can they be seated if 3 people have to sit together?
iv. i am on the committee and can't stand 2 of the members. how many seating arrangements can be made if I cannot sit next to either of these 2?

1 There are 40 people on the this information to answer the following questions. faculty. Of these 40, 15 are men and 25 are women. Use 3. A committee of 8 is to be selected by the principal. How many possible committees can be created, regardless of gender? a. b. What is the probability that the principal selects a committee that contains i. All men ii. All women iii. 4 men and 4 women iv. At least 2 men v. No more than 3 men ts vi. 5 women and 3 men to find the p The principal now has his 8 members. Answer the following questions about these 8. Assume only 8 chairs for them to sit. c. i. If they sit at a large table (in a line), how many ways can they be seated? li. How many ways can they be seated in a circle? ili. If they are in a line, how many ways can they be seated if 3 people have to sit together? iv. I am on the committee and can't stand 2 of the teachers. How many seating arrangements can be made if I cannot sit next to either of these 2?

Explanation / Answer

Given

There are 40 people on the faculty.

Of the 40, 15 are men and 25 are women

a) A committee of 8 is to be selected by the principal. How many possible committees can be created, regardless of gender?

No of ways that a committe of 8 members can form is we have to select 8 members from 40 members given that regardless of gender = 40C8

b) i). all men

we have to select all 8 men for the 8 men committe

total members present = 15

of these we have to select 8 members

No of ways = 15C8

ii) all women

toatl no of women = 25

total no. of ways = 25C8

iii)4 men and 4 women

there are 25 women and 15 men

no of ways = 25C4 * 15C4

iv) at least 2 men

atleast 2 men means selecting 2 or more men i.e(2,3,4,5,6,7,8)

no . of ways = 15C2 *25C6 + 15C3 * 25C3 +15C4 * 25C4 + 15C5 *25C3 + 15C6 * 25C2 + 15C7 * 25C1 + 15C8

v) no more than 3 men

No more than 3 men means less than 3 men to be selected i.e( 0 , 1 , 2 , 3 )

no. of ways = 25C8 + 25C7 * 15C1 + 25C6 * 15C2 + 25C5 * 15C3

vi). 5 women and 3 men

No . of ways = 25C5 * 15C 3

C) The principal now has his 8 members. Answer the following questions about these 8. Assume only 8 chairs for them to sit.

i. if they sit at large table (in a line), How many ways can they be seated?

8 members are selected we have to arrange the in 8 seats = 8! ways

ii. how many ways can they be seated in a circle?

8 members are to be seated in 8 seats in circle = (8-1)!

= 7!

iii)if they are in a line, how many ways can they be seated if 3 people have to sit together?

the group of 3 people can be taken as 1

then total no . of ways = 5 people + 1 group

= 6! ways

  

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