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 :
Solution:
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
$ = (\,{}^5C_1\,{}^5C_2\,{}^5C_2) \cdot 3 + (\,{}^5C_1\,{}^5C_1\,{}^5C_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 |