Question

Probability question - please help!
We need to choose a sampling of vehicles for analysis. We have a list of 38 passenger
cars and 27 pickup trucks.
How many total ways are there to choose 4 passenger cars and 3 pickup trucks with
the extra condition of choosing a lead vehicle that is a pickup truck?

Answer 1

take combinations in use

Answer 2

i'm not sure what you mean?

Answer 3

How do you do this question? Sorry, I'm a freshman but I love to help people out! (:

Answer 4

What's a "lead vehicle"?

Answer 5

It comes first - so, this woud take order into consideration.

Answer 6

I don't quite get it... you will always choose 4 pickup trucks and 3 cars.

\[\Large {38 \choose 4}{27 \choose 3} \]

If order matters, it's \[\Large _{38}P_4 \cdot_{27}P_3\]

... I think. Hmm.

Answer 7

I came up with the same answer, but it doesn't make sense. If we have the qualifying factor of placing an order, we should theoretically come up with less options than not placing an order, but this response has MORE options.
If we did simply 38ncr4*27ncr3 = 2.1E8, but with the order you outlined, our answer would be something to the effect of 38ncr4*27nPr3 = 1.2E9

Answer 8

Actually, if order matters, we'll end up with more combinations since any ABCD combination (that you'd get by using nCr) would actually have the following combinations using nPr:
ABCD
ABDC
ACBD
ACDB
ADBC
ADCB

BACD
BADC
BCAD
BCDA
BDAC
BDCA

... and so on.

However, I think that the last bit about "the extra condition of choosing a lead vehicle that is a pickup truck" might be there to just throw you off. I don't think it makes any difference to the nCr answer.