There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is :

Question

There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is : (A) 1500 (B) 2255 (C) 3000 (D) 2250

Tardigrade Admin · Accepted Answer

A B C underline5 underline5 underline5 1 2 2 2 1 2 2 2 1 1 1 3 1 3 1 3 1 1 Total number of selection = ( 5C1 5C2 5C2) ⋅ 3 + ( 5C1 5C1 5C3)⋅ 3 =5 ⋅ 10 ⋅ 10 ⋅ 3 + 5⋅ 5 ⋅ 10 ⋅ 3 = 2250

Q. There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is :

1500

2255

3000

2250

A B C

$\underline{5}$ $\underline{5}$ $\underline{5}$

1 2 2

2 1 2

2 2 1

1 1 3

1 3 1

3 1 1

Total number of selection
$= (^{5} C_{1}^{5} C_{2}^{5} C_{2}) \cdot 3 + (^{5} C_{1}^{5} C_{1}^{5} C_{3}) \cdot 3$
$= 5 \cdot 10 \cdot 10 \cdot 3 + 5 \cdot 5 \cdot 10 \cdot 3$
$= 2250$

A	B	C
$\underline{5}$	$\underline{5}$	$\underline{5}$
1	2	2
2	1	2
2	2	1
1	1	3
1	3	1
3	1	1