Question

A examination question paper consists of 12 questions divide into part A and part B.part A consists of 7 questions and part B consists of 5 questions.In how many ways can a student answer 8 questions in the examination if
a.there is no condition put in the paper
b the student has to answer 5 from part A and 3 from part B​

Answer 1

There are 5 question in parts & 7 question in parts 2

atleast 8 question have to we attempted & 3 from lach part.

There are 3 options

(1)3 from part 1 & % from part 2

no, of ways

=

5

C

3

×

7

C

5

=

3!(5−3)!

5!

×

5!(7−5)!

7!

=

2

5×4

×=

2

7×6

=5×2×7×3

=210 ways

(2)4 from part 1 & 4 from part 2

=

5

C

4

×

7

C

4

=

4!(5−4)!

5!

×=

4!(7−4)!

7!

=5×=

3×2×1

7×6×5

=5×7×5

=175 ways

(3)5 from part 1 & 3 from part 2

=

5

C

5

×

7

C

3

=

5! 0!

5!

×=

3!(7−3)!

7!

=1×=

3×2

7×6×5

=35 ways

Total number of ways =210+175+35

420 ways