Question
A student has a cup with 14 writing implements: 7 pencils, 5 ball point pens, and 2 felt-tip pens.
In how many ways can the student select 4 writing implements? = C(14,4) = 1001
In how many ways can the selection be made if no more than one ball point pen is selected?
In how many ways can the student select 4 writing implements? = C(14,4) = 1001
In how many ways can the selection be made if no more than one ball point pen is selected?
Answers
drwls
First of all, C(14,4) is not 1001.
The only combinations possibilties are:
PPP (3 pencils)
PPF (2 pencils and 1 felt-tip)
PPB (2 pencils and 1 ballpoint, etc)
BBB
BBP
BBF
FFP
FFB (the least likely result)
PBF
Different permutations of the same group of three don't count as being different.
That is a total of only 9 possibilities.
The probabilities of each will not be the same.
The only combinations possibilties are:
PPP (3 pencils)
PPF (2 pencils and 1 felt-tip)
PPB (2 pencils and 1 ballpoint, etc)
BBB
BBP
BBF
FFP
FFB (the least likely result)
PBF
Different permutations of the same group of three don't count as being different.
That is a total of only 9 possibilities.
The probabilities of each will not be the same.