The board of a large company is made up of 7 women and 9 men. 6 of them will go

Question

The board of a large company is made up of 7 women and 9 men. 6 of them will go as a delegation to a national conference. a) How many delegations are possible? b) How many of these delegations have all men? c) How many of these delegations have at least one woman? The math club at a certain school has 10 members, of which 6 are seniors and 4 juniors. In how many ways can they form a group of 5 members to go to a tournament, if at least 4 of them have to be seniors (aka either a group of 4 seniors and 1 junior, or a group of 5 seniors? There are 60 students in Math410. I want to choose a group of students to go to a meeting. In how many ways can I make this group, if it has to be either 4 or 5 students? There are 10 students in a classroom. The teacher is going to select a group of them to leave the room. a) In how many ways can the teacher select a group of 4 students to leave the room? b) In how many ways can the teacher select the group of 6 students to stay in the room? c) In how many ways can the teacher select a group of students, if there are no restrictions on the size of the group that leaves (allowing also the extreme cases where no students or all students leave)? Using a 52 card deck, how many different collections (hands) of 5 cards are there? Using a 52 card deck, how many 5 card hands have either 5 hearts or 4 hearts and 1 club? In how many ways can 4 married couples attending a concert be seated in a row of 8 seats if: a) There are no restrictions? b) Each married couple is seated together?

Explanation / Answer

4) 7 women , 9 men

, 6 of them will be selected ,

we have to select 6 persom from (9+7) = 16 person

hence nuber of ways = 16 C 6 = 16!/((16-6)!*6!) = 16! /(10!*6!) = 8008

b) all men - we have to select 6 men from 9 men.

= 9C6 = 9!/(3!*6!) = 84

c) at least one woman = total number of ways - number of ways when are 6 are male = 8008 -84 = 7924

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.