P & C Problem

[agni_h1]

Q.A teacher prepares a test.She gives 5 objective type qs ot of which 4 need 2b answered.Find the total ways in which it can be answered if first 2 qs have 3 choices and last 3 have 4 choices.

a.255
b.816
c.192
d.100
e.194

Ans:B

I am getting 1680.Please help

[kmittal82]

Good question

Lets say the questions are a b c d e

case 1:

You select a and b, and 2 out of c d e

Total number of ways of selecting 2 out of cde = 3c2 = 3

Total number of ways of answering questions in this = 3 x 3 x 4 x 4 x 4 x 3 = 432

The 3 is in bold because that's the possible combinations of picking 2 questions out of c d and e

case 2:

You select c d e, and 1 out of a or b

Total number of ways of answering = 4 x 4 x 4 x 3 x 2 = 384

The 2 is in bold because that's the possible combinations of picking 1 question from a and b

Thus, total ways = case1 + case 2 = 432 + 384 = 816

[Stuart@KaplanGMAT]

Q.A teacher prepares a test.She gives 5 objective type qs ot of which 4 need 2b answered.Find the total ways in which it can be answered if first 2 qs have 3 choices and last 3 have 4 choices.

a.255
b.816
c.192
d.100
e.194

Ans:B

I am getting 1680.Please help

People take a lot of time to post solutions and help others study for the GMAT. Please take the time to fully type out your questions in english.

[agni_h1]

@kmittal:Thanks for the explanation
@Stuart: I will make sure I take my time to fully type the question next time.

[agni_h1]

Good question

Lets say the questions are a b c d e

case 1:

You select a and b, and 2 out of c d e

Total number of ways of selecting 2 out of cde = 3c2 = 3

Total number of ways of answering questions in this = 3 x 3 x 4 x 4 x 4 x 3 = 432

The 3 is in bold because that's the possible combinations of picking 2 questions out of c d and e

case 2:

You select c d e, and 1 out of a or b

Total number of ways of answering = 4 x 4 x 4 x 3 x 2 = 384

The 2 is in bold because that's the possible combinations of picking 1 question from a and b

Thus, total ways = case1 + case 2 = 432 + 384 = 816

There was a small typo in your answer. For case 1, the the result is = 3 x 3 x 4 x 4 x 3

I was thinking in a totally different way. I was selecting 4 questions out of five and then finding the number of ways for each.Didn't work out that way.