Question

From a group of 9 biologists and 5 chemists a group of 3 biologists and 2 chemists is to be formed. In how many ways can this be done if;

- Any biologist and any chemist can be included?
- One particular chemist must be in the group?
- 3 particular biologists cannot be in the group?

Answer #1

1. In how many ways can 10 objects be split into two
groups containing 4 and 6 objects, respectively?
2. In how many ways can a committee of 5 people be chosen out of 9
people?
3. Out of 5 mathematicians and 7 physicists, a committee consisting
of 2 mathematicians and 3 physicists is to be formed. In how many
ways can this be done if (a) any mathematician and any physicist
can be included, (b) one particular physicist must...

In a group of 2 freshmen, 3 Sophomores, and 10 Junior
in how many
ways 5 students be chosen if:
a. regardless of their year level?
b. the two freshmen must be included?
c. the two freshmen must be excluded?
d. there must be at least 4 juniors?
e.there must be at most 3 sophomores?

1. From a group of 6 Canadians, 9 Australians and 5
Italians, exactly 3 Canadians, 4 Australians and 2 Italians are to
be selected to form a committee. How many different working
committees can be formed if one specific Australian (named
Charlotte) and one specific Italian (named Marco) refuse to work
together (call this event A)?
5. Consider two manufacturing machines, A and B. It is
known that machine A has a defect rate 3 times larger than machine
B....

1. Twelve individuals want to form a committee of four.
(a.) How many committees are possible?
(b.) The 12 individuals consist of 5 biologists, 4 chemists, and
3 physicists. How many committees consisting of 1 biologist, 1
chemist, and 2 physicists are possible?
(c.) In the setting of part (b), if all committees are equally
as likely, what is the probability the committee formed will
consist of 1 biologist, 1 chemist, and 2 physicists?
2. You are out of town...

Suppose there are 9 people (named A-I)
How many different ways can they be grouped into 5?
How many different ways can they be grouped into 5 if A must be
included?

How many 4-digit numbers can be formed from the digits 2, 3, 8
and 9?

ind the number of ways of selecting 12 balls from 6 red bal
COMBINATION
Solve each of the following problems. (Show your work.)
Find the number of ways of selecting 12 balls from 6 red balls,
5 white balls and 5 blue balls if each selection consists of 4
balls of each color.
Among the seven nominees for two vacancies on the city council
are four men and six
women. In how many ways may these vacancies be filled...

9) In a panel discussion with 3 industry employees, 2 government
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a) …with no restrictions (each person can sit anywhere)?
b) …if the 3 industry employees must sit together (in any order)
to the right of the others (also in any order)?
c) …if, prior to sitting, each of the industry employees is
paired up with a partner and these pre-assigned pairs must stay
together...

a. i. 12 people are to be divided into a group of 6, a group of
4 and a group of 2. in how many different ways can this be
done?
ii. Determine the number of different arrangements that can be
made of all 9 letters in the word CAMERAMAN in each of the
following cases.
- There are no restrictions
- The A's occupy the 1st, 5th and 9th positions
- There is exactly one letter between the M's

How many ways a team of five salespersons can be
formed from a group of 10 salesmen and 8 saleswomen, if the team
contains at most 2 saleswomen?

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