Combinations help

ksmith3894

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Rework problem 7 from section 2.3 of your text. Assume that the student has a cup with 15 writing implements: 8 pencils, 5 ball point pens, and 2 felt-tip pens.(1) In how many ways can the student select 2 writing implements?

(2) In how many ways can the selection be made if no more than one ball point pen is selected?

and

There is a chairperson who must select a subcommittee but assume that the committee consists of 11 people including the chairperson and that the chairperson must select a committee of 3 people from the other 10 members of the committee.
In how many ways can this be done?
 
Rework problem 7 from section 2.3 of your text. Assume that the student has a cup with 15 writing implements: 8 pencils, 5 ball point pens, and 2 felt-tip pens.(1) In how many ways can the student select 2 writing implements?

(2) In how many ways can the selection be made if no more than one ball point pen is selected?

and

There is a chairperson who must select a subcommittee but assume that the committee consists of 11 people including the chairperson and that the chairperson must select a committee of 3 people from the other 10 members of the committee.
In how many ways can this be done?

1) List the possible ways you can select two writing implements:

1 pencil & 1 ball point pen

1 pencil & 1 felt-tip pen

2 pencils

1 felt-tip pen & 1 ball point pen

and continue....

Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.
 
Combinations

In the first problem for Assume that the student has a cup with 15 writing implements: 8 pencils, 5 ball point pens, and 2 felt-tip pens.

I got (1) In how many ways can the student select 2 writing implements? 105 by C (15,2)

In how many ways can the selection be made if no more than one ball point pen is selected?
Dont know about this
 
Hello, ksmith3894!

Since the subject line says "Combinations",
I assume you are familiar with them.


A student has 8 pencils, 5 ballpoint pens, and 2 felt-tip pens.
(1) In how many ways can the student select 2 writing implements?

There are 15 objects; he will select 2 of them.

The number of ways is: .\(\displaystyle _{15}C_2 \:=\:\dfrac{15!}{2!\,13!} \:=\:105\)



(2) In how many ways can the selection be made
. . . if no more than one ballpoint pen is selected?

There are 5 ballspoint pens and 10 Others.

There are two cases to consider.

(a) 0 ballpoint pens and 2 Others.
. . .There are: .\(\displaystyle \left(_5C_0\right)\left(_{10}C_2\right) \:=\:45\) ways.

(b) 1 ballpoint pen and 1 Other.
. . .There are: .\(\displaystyle \left(_5C_1\right)\left(_{10}C_1\right) \:=\:50\) ways.

Therefore, there are: \(\displaystyle 45 + 50 \:=\:95\) ways.



A committee of 3 people is to be selected from 10 volunteers.
In hw many ways can this be done?

Answer: .\(\displaystyle _{10}C_3 \:=\:\dfrac{10!}{3!\,7!} \:=\:120\) ways.
 
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