Permutation question

[goelmohit2002]

In a certain test, a student must answer 8 out of 10 questions. How many choices are there if atleast 4 of the first 5 questions must be answered ?

OA = after some discussion.

[supratims]

From the first 5 questions he can choose 4 in 5C4 = 5 ways.
From the second set of 5, he can choose 4 in 5C4 = 5 ways,
total number of ways = 5*5 = 25

what says the OA ?

[goelmohit2002]

OA = 35

[sundar.kms]

The question states that atleast 4 questions from the first 5.

So in the first instance the student can select 4 questions from 5 questions in 5C4 ways and from the remaining questions he/she can choose 4 questions in 5C4 ways. So probability becomes 5C4*5C4 = 25 ways.

In second instance the student chooses all 5 questions from the first 5 questions in 5C5 ways and 3 questions from the remaining 5 questions in 5C3 ways = 5C5*5C3 = 10

So overall probability = 25 + 10 = 35 ways.

[supratims]

Perfect ! I missed out on that one.

[StaceyKoprince]

Please post the source of this question. We cannot host questions if credit is not given to the author of the question. Thanks.