A reading list for a certain course consists of 10 books, of which 4 a

Possibilities include
1novel, 3 poems
6! / 1!5! × 4! /3! 1! =24

2 novels, 3 poems
6!/2! 4! × 4!/2! 2! =90

0 novels, 4 poems
=1

24+90+1=115

B. 115

Novel=N,Poem book=P; therefore 10=4+Novels =>N=6;P=4

The final selection would be = 2N and 2P +1N and 3P + 4P =6C2*4C2 + 6C1*4C3 + 4C4 = 90+24+1=115

Hence answer is B

Thanks,

Options with two novels: 6C2 * 4C2 = 90

Options with one novel: 4C3 * 6C1 = 24

Option with no novel: 4C4 = 1

so 90+24+1 = 115

Answer is B

Required selection=(4C2*6C2)+(6C1*4C3)+(4C4)
=90+24+1
=115
Answer B

We are given that a course reading list contains 4 poems and 6 novels. We need to determine the number of ways a student can select 4 books if at most 2 novels can be selected.

Scenario one: 4 poems are selected.

4 poems can be selected in 4C4 = 1 way.

Scenario two: 1 novel and 3 poems are selected.

3 poems can be selected in 4C3 = 4!/[3!(4-3)!] = (4 x 3 x 2)/3! = 4 ways, and 1 novel can be selected in 6C1 = 6 ways.

Thus, 3 poems and 1 novel can be selected in 4 x 6 = 24 ways.

Scenario three: 2 novels and 2 poems are selected.

2 poems can be selected in 4C2 = 4!/[2!(4-2)!] = (4 x 3)/2! = 6 ways, and 2 novels can be selected in 6C2 = 6!/[2!(6-2)!] = (6 x 5)/2! = 15 ways.

Thus, 2 poems and 2 novels can be selected in 6 x 15 = 90 ways.

All 4 books with at most 2 novels can be selected in 1 + 24 + 90 = 115 ways.

Answer: B

Total: 4B and 6N
Possible outcomes (2B,2N) + (3B,1N) + (4B)
4!/2!*2! * 6!/4!*2! + 4!/3!*1! * 6!/1!*5! + 4!/4! = 90 + 24 +1 = 115. Answer (B)

We can break this problem into scenarios:

Scenario 1: 2 biographies and 2 novels

The number of ways to select 2 biographies is 4C2 = 4!/[2! x (4 - 2)! = 4!/(2! x 2!) = (4 x 3)/2! = 6.

The number of ways to select 2 novels is 6C2 = 6!/[2! x (6 - 2)!]= 6!/(2! x 4!) =(6 x 5)/2! = 15.

So there are a total of 6 x 15 = 90 ways for this scenario.

Scenario 2: 3 biographies and 1 novel

The number of ways to select 3 biographies is 4C3 = 4.

The number of ways to select 1 novels is 6C1 = 6.

So there are a total of 4 x 6 = 24 ways for this scenario.

Scenario 3: 4 biographies

The number of ways to select 4 biographies is 4C4 = 1.

So there is only 1 way for this scenario.

So there are a total of 90 + 24 + 1 = 115 ways to choose 4 books that consist 2 or more biographies.

Answer: B

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