Help needed..?

Question

1) In how many different ways could you fill out an answer sheet for a multiple choice test with 5 questions where each question has 4 different answers?

In how many ways could you fill out the answer sheet if you have the option of leaving as many questions as you like unanswered?


2)
Pat must take 4 courses from a list of 3 language courses and 7 science courses.
In how many different ways can she select the four courses?
In how many different ways can she select the four courses if she must choose 2 language courses and 2 science courses?
In how many different ways can she select the four courses if she must choose at least one language course?

Answer 1

From me you get HELP not answers......Think them out...

1) Question a) has 4 possible answers
Question b) has 4 possible answers.... and so on

If you just had two questions how many possible ?
for each one in the first question you had 4 in the second so that would be 4 x 4 or 16.

if you just had 3 questions there would be another 4 possible groups so it would be 4 x 4 x 4 or 64.

got the idea?


for the second part of the first question... pretend that leaving it blank is the same as 'none of the above' or a 5th answer

two questions would give you
5 x 5 or 25

three would give you 5 x 5 x 5 or 125.. and so on.


Question 2 is a little different

In the first part Pat just has to choose 4 from 10 right?

if she takes the first one there are 9 left (since she can not take the same class twice)... then 8... then 7

so... unlike the first problem her options are reduced each time
(a factorial in case you were looking for a name)

picking just 1... 10 options
picking just 2 .. 10 x 9 options = 90

and so on...

in the second part she has two different selections

2 out of 3 and (PLUS) 2 out f 7

so..

3*2 gives you 6 possibe combinations in language.. and so on.

ok.. that shoudl be enough to get you going.